For completeness, I just tested the combination Gradle 3.4.1 and OpenJDK 11, all from current Bionic (updated):

* I get the "WARNING: An illegal reflective access" spamming in the console. Reported separately:
  https://bugs.launchpad.net/ubuntu/+source/gradle/+bug/1803855
* The build breaks with
> Failed to notify project evaluation listener.
   > javax/xml/bind/annotation/XmlSchema

The full exception is:
org.gradle.api.ProjectConfigurationException: A problem occurred configuring project ':sample-integration-android'.
        at org.gradle.configuration.project.LifecycleProjectEvaluator.addConfigurationFailure(LifecycleProjectEvaluator.java:94)
        at org.gradle.configuration.project.LifecycleProjectEvaluator.notifyAfterEvaluate(LifecycleProjectEvaluator.java:89)
        at org.gradle.configuration.project.LifecycleProjectEvaluator.doConfigure(LifecycleProjectEvaluator.java:76)
        at org.gradle.configuration.project.LifecycleProjectEvaluator.access$000(LifecycleProjectEvaluator.java:33)
        at org.gradle.configuration.project.LifecycleProjectEvaluator$1.execute(LifecycleProjectEvaluator.java:53)
        at org.gradle.configuration.project.LifecycleProjectEvaluator$1.execute(LifecycleProjectEvaluator.java:50)
        at org.gradle.internal.Transformers$4.transform(Transformers.java:169)
        at org.gradle.internal.progress.DefaultBuildOperationExecutor.run(DefaultBuildOperationExecutor.java:106)
        at org.gradle.internal.progress.DefaultBuildOperationExecutor.run(DefaultBuildOperationExecutor.java:61)
        at org.gradle.configuration.project.LifecycleProjectEvaluator.evaluate(LifecycleProjectEvaluator.java:50)
        at org.gradle.api.internal.project.DefaultProject.evaluate(DefaultProject.java:599)
        at org.gradle.api.internal.project.DefaultProject.evaluate(DefaultProject.java:125)
        at org.gradle.execution.TaskPathProjectEvaluator.configure(TaskPathProjectEvaluator.java:35)
        at org.gradle.execution.TaskPathProjectEvaluator.configureHierarchy(TaskPathProjectEvaluator.java:62)
        at org.gradle.configuration.DefaultBuildConfigurer.configure(DefaultBuildConfigurer.java:38)
        at org.gradle.initialization.DefaultGradleLauncher$ConfigureBuildAction.execute(DefaultGradleLauncher.java:233)
        at org.gradle.initialization.DefaultGradleLauncher$ConfigureBuildAction.execute(DefaultGradleLauncher.java:230)
        at org.gradle.internal.Transformers$4.transform(Transformers.java:169)
        at org.gradle.internal.progress.DefaultBuildOperationExecutor.run(DefaultBuildOperationExecutor.java:106)
        at org.gradle.internal.progress.DefaultBuildOperationExecutor.run(DefaultBuildOperationExecutor.java:56)
        at org.gradle.initialization.DefaultGradleLauncher.doBuildStages(DefaultGradleLauncher.java:160)
        at org.gradle.initialization.DefaultGradleLauncher.doBuild(DefaultGradleLauncher.java:119)
        at org.gradle.initialization.DefaultGradleLauncher.run(DefaultGradleLauncher.java:102)
        at org.gradle.launcher.exec.GradleBuildController.run(GradleBuildController.java:71)
        at org.gradle.tooling.internal.provider.ExecuteBuildActionRunner.run(ExecuteBuildActionRunner.java:28)
        at org.gradle.launcher.exec.ChainingBuildActionRunner.run(ChainingBuildActionRunner.java:35)
        at org.gradle.launcher.exec.InProcessBuildActionExecuter.execute(InProcessBuildActionExecuter.java:41)
        at org.gradle.launcher.exec.InProcessBuildActionExecuter.execute(InProcessBuildActionExecuter.java:26)
        at org.gradle.tooling.internal.provider.ContinuousBuildActionExecuter.execute(ContinuousBuildActionExecuter.java:75)
        at org.gradle.tooling.internal.provider.ContinuousBuildActionExecuter.execute(ContinuousBuildActionExecuter.java:49)
        at org.gradle.tooling.internal.provider.ServicesSetupBuildActionExecuter.execute(ServicesSetupBuildActionExecuter.java:49)
        at org.gradle.tooling.internal.provider.ServicesSetupBuildActionExecuter.execute(ServicesSetupBuildActionExecuter.java:31)
        at org.gradle.launcher.daemon.server.exec.ExecuteBuild.doBuild(ExecuteBuild.java:67)
        at org.gradle.launcher.daemon.server.exec.BuildCommandOnly.execute(BuildCommandOnly.java:36)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.WatchForDisconnection.execute(WatchForDisconnection.java:47)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.ResetDeprecationLogger.execute(ResetDeprecationLogger.java:26)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.RequestStopIfSingleUsedDaemon.execute(RequestStopIfSingleUsedDaemon.java:34)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.ForwardClientInput$2.call(ForwardClientInput.java:74)
        at org.gradle.launcher.daemon.server.exec.ForwardClientInput$2.call(ForwardClientInput.java:72)
        at org.gradle.util.Swapper.swap(Swapper.java:38)
        at org.gradle.launcher.daemon.server.exec.ForwardClientInput.execute(ForwardClientInput.java:72)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.LogAndCheckHealth.execute(LogAndCheckHealth.java:55)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.LogToClient.doBuild(LogToClient.java:60)
        at org.gradle.launcher.daemon.server.exec.BuildCommandOnly.execute(BuildCommandOnly.java:36)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.EstablishBuildEnvironment.doBuild(EstablishBuildEnvironment.java:72)
        at org.gradle.launcher.daemon.server.exec.BuildCommandOnly.execute(BuildCommandOnly.java:36)
        at org.gradle.launcher.daemon.server.api.DaemonCommandExecution.proceed(DaemonCommandExecution.java:120)
        at org.gradle.launcher.daemon.server.exec.StartBuildOrRespondWithBusy$1.run(StartBuildOrRespondWithBusy.java:50)
        at org.gradle.launcher.daemon.server.DaemonStateCoordinator$1.run(DaemonStateCoordinator.java:297)
        at org.gradle.internal.concurrent.ExecutorPolicy$CatchAndRecordFailures.onExecute(ExecutorPolicy.java:63)
        at org.gradle.internal.concurrent.StoppableExecutorImpl$1.run(StoppableExecutorImpl.java:46)
Caused by: org.gradle.internal.event.ListenerNotificationException: Failed to notify project evaluation listener.
        at org.gradle.internal.event.AbstractBroadcastDispatch.dispatch(AbstractBroadcastDispatch.java:55)
        at org.gradle.internal.event.BroadcastDispatch.dispatch(BroadcastDispatch.java:79)
        at org.gradle.internal.event.BroadcastDispatch.dispatch(BroadcastDispatch.java:30)
        at org.gradle.internal.dispatch.ProxyDispatchAdapter$DispatchingInvocationHandler.invoke(ProxyDispatchAdapter.java:93)
        at com.sun.proxy.$Proxy15.afterEvaluate(Unknown Source)
        at org.gradle.configuration.project.LifecycleProjectEvaluator.notifyAfterEvaluate(LifecycleProjectEvaluator.java:82)
        ... 56 more
Caused by: java.lang.NoClassDefFoundError: Could not initialize class com.android.sdklib.repository.AndroidSdkHandler
        at com.android.builder.sdk.DefaultSdkLoader.init(DefaultSdkLoader.java:377)
        at com.android.builder.sdk.DefaultSdkLoader.getSdkInfo(DefaultSdkLoader.java:360)
        at com.android.build.gradle.internal.SdkHandler.initTarget(SdkHandler.java:133)
        at com.android.build.gradle.BasePlugin.ensureTargetSetup(BasePlugin.java:671)
        at com.android.build.gradle.BasePlugin.createAndroidTasks(BasePlugin.java:570)
        at com.android.build.gradle.BasePlugin.lambda$null$4(BasePlugin.java:526)
        at com.android.builder.profile.ThreadRecorder.record(ThreadRecorder.java:81)
        at com.android.build.gradle.BasePlugin.lambda$createTasks$5(BasePlugin.java:522)
        at org.gradle.internal.event.BroadcastDispatch$ActionInvocationHandler.dispatch(BroadcastDispatch.java:93)
        at org.gradle.internal.event.BroadcastDispatch$ActionInvocationHandler.dispatch(BroadcastDispatch.java:82)
        at org.gradle.internal.event.AbstractBroadcastDispatch.dispatch(AbstractBroadcastDispatch.java:44)
        ... 61 more