Can a loose A/C belt cause it A/C problems

I just bought a 1996 Geo Sedan and was told the A/C only needed a belt. However, there is currently a belt and appears to be engaging as would be expected.

Is it possible that the A/C will not run if the incorrect belt is there? I have not spoken to the Mechanic (he is on vacation) yet but the girl I bought it from said the mechanic said he was not able to find the correct belt but kept it in place until the correct one could be bought from Chevy. Chevrolet want $70 for it but the local parts shop says only $16 but he did not ask if it had Power steering (which the Chevy place did). Is it a different belt if you have PS vs no PS?

I did just get the 2-volume service manual today but found nothing specific about the belt size.

Not sure if the belt runs your p/s pump too. If it does and it was loose you'd be having problems with you p/s and the belt should be squealing especially when you turn the air on. Could possibly need a charge instead of a belt. I know from experience if you don't get your a/c belt tight enough it will squeal and I wouldn't know why a mechanic would leave a loose belt on that's just asking for trouble if it comes off it could take another belt with it.