89 Mercury Grand Marquis - yank the AC belt?

I just bought my 16-year-old daughter her first car: a 1989 Mercury Grand Marquis LS 5.0-liter engine from the proverbial little old lady original owner. Except for the fact that the AC doesn't work, it runs really well -- EXCEPT the AC belt squeals horribly when you first turn on the car. Tire Kingdom quoted me $250 to replace it -- yeah, right. But I noticed that it has a separate belt for the alternator. We don't intend to spend money to repair the AC -- so why couldn't we just take the AC belt off? Would the car still run OK?
Thanks alot for any help you can give me!