The aftermarket stereo will have to control the bose amp in order for it to play music at all unless the previous owner re wired the entire car. Which if its cheap i doubt highly that he did. The stock amplifier has to be turned on by the head unit to create any sound. This is done through the control wire. Which should be the bright pink wire in second plug of the factory wiring harness.
As for whether of not the other stereo would work, the easiest way to tell will probably be to post pictures of it up on here and me and others can compare it to grand prix stereos and decide. Theres a good chance it will work as long as its in the same year range as the GP, and it is. However theres no guarantee you wont have to modify it to turn your amplifier on. This is because theres a third plug on the back of the Bose stereo aside from the antenna and the main harness plug. The second plug controls the amplifier and it receive signals from the interior lights telling it when to dim or shut off with the rest of the lights. It also puts out some of the signals for the RAP system in the GP. Oldsmobile may or may not use a plug like this.
I don't know since the only olds ive worked on are my girlfriends bravada and i havent swapped stereos on it, just all the speakers for her birthday. and a 67 cutlass which quite obviously didn't even have a place to put a new stereo. I think your best bet would be to just buy a better after market unit.
. GM made 2 versions, The Bose
(which you have) and just the plain ol cd player radio
. Good luck getting it unlocked, I believe theres instructions in your owners manual that tells you how to get it unlocked.
