When your NA motor starts to sound supercharged...
Your alternator is screwed. It isn’t dead yet, it might not even die soon, but it sure sounds like it is on its death bed. For those of you who have luckily not experienced this problem, Bonne’* seem to dislike alternators. I went through 3 of them on my 1994 SSE. And, my 1997 SSE was on its 2nd alternator when I sold it.
As for that obnoxious whine, it can actually be attributed to wear in the rear bearing of the alternator. Although, it is not damaging your car, it certainly damages the ears. I know on my 1997 SSE, the noise was worse when the car was cold, and as the car warmed up it would quiet down. As it turned out, within a year my alternator went and I tossed in a 160 amp replacement (I think stock is 105). After that, there was no more noise and no more problems.
Notes: Both the 1994 and 1997 SSE’* were bone stock. On every occasion the alternator needed to be replaced after the GM warranty had expired.