VirtualDJ LE does not quantize hot cues at all. With Smart looping enabled, it does not quantize the loop-in point either, but quantizes the loop-out point to the closest beat (relative to the loop-in point,) unless it's within a beat's distance, in which case the loop-out point goes to the closest 1/8 beat. (So a Smart loop is always a quantized _length_ in terms of beats, but where it starts is never quantized.)
As for beatloops, VDJ starts the loop exactly where the cursor is when you click the button (since loop-in is not quantized) and just makes the loop x beats long.
VirtualDJ LE does not quantize hot cues at all. With Smart looping enabled, it does not quantize the loop-in point either, but quantizes the loop-out point to the closest beat (relative to the loop-in point,) unless it's within a beat's distance, in which case the loop-out point goes to the closest 1/8 beat. (So a Smart loop is always a quantized _length_ in terms of beats, but where it starts is never quantized.)
As for beatloops, VDJ starts the loop exactly where the cursor is when you click the button (since loop-in is not quantized) and just makes the loop x beats long.