If I take an audio track, change the output level, and tell Vegas to render to a new track, then Vegas has gone in and taken each sample (typically a 16-bit number) and computed a new sample value. If I do this multiple times, then presumably I will eventually be able to hear artifacts, since the resulting waveform starts to differ from the original.

I guess I could just do a test myself, but am assuming some of you guys already have a working knowledge of this issue.

Perhaps this is one reason why pros often work with 24-bit samples--the degradation is relatively minor unless many re-renders are performed.