How likely is it for a generator to "blow" a sound system if there is no music and just people talking with the use of a microphone?
Well the question is what generator and what equipment?
If it was a special from Home Depot very likely, as they generally have very rough wave forms, no voltage regulation and lots of noise on the signal.
When you scope them they look awful. A pro generator, with pro voltage regulation, then less likely. However for most generators, a good UPS with tight voltage control and fast switch to battery back up is strongly recommended for any equipment with solid state ICs and especially micro processors.