I don't know which GTP you are referring to, but I owned a 2004 Grand Prix GTP (series III 3800/eaton SC) a few years ago, and that had no SC whine at idle. If it does, it either isn't stock, or isn't running right. You really had to lay into it before the SC whine became prominent.
I have a Series II 3800, and mine is the same as yours. There is no whine, I can't even hear it at full boost.