This is not just about Arabic glyphs. It may be about the way Google presents the fonts as when you download from the website the default is to only download Latin characters. This is definitely a problem for Typecatcher with Thai as well. I noticed a font with a Thai name and added some custom Thai text, but it only shows in an installed font, not the selected Google font (Sriracha in this case).
This is not just about Arabic glyphs. It may be about the way Google presents the fonts as when you download from the website the default is to only download Latin characters. This is definitely a problem for Typecatcher with Thai as well. I noticed a font with a Thai name and added some custom Thai text, but it only shows in an installed font, not the selected Google font (Sriracha in this case).