You can take the S/C belt off, and the car will be able to run(not under normal daily driving conditions) . but like said early it will become really rich and wouldn't perform well at all.

I ran a couple of days with by S/C belt off of my grand prix. The belt broke and being it was a special size (I droped down a pulley size) I had to order a new one. It made the driveability worse as well as the gas milage, but it got me from point A to B.