What happens if ac compressor goes out in car?

clearly, the air conditioning will quit working, but the common because of compressor failure is the clutch locking up. This will because the belt to break shortly after the clutch locks. This in turn can because a range of other problems based on what that belt drives. Functionally for the car, it isn't needed. you may be able to get a differ ant belt, and path around the compressor and the car should operate just good.

Before the AC typically stops working the bearing will go and it'll squeal
Unless you have to add more freon

There's some number of reasons this may happen. Low refrigerant, flawed controls, flawed clutch or fuse.
A/C compressors are pretty well built so look for other causes 1st. You want to be sure it is not the compressor before you replace it.

When they "chagre" your ac system they also add oil to the refirdgerant. If the ac is blowing hot air you have a leak they'll inject dye and coolant and see where it leaks and fix it.
If it has a brken belt the compressor locked up and you'll have to have it replaced and the system rechagred.
Compressors on hondas go out frequntley it's common. I used to sell a lot of them when I worked for a honda fix place.

If you thake out the ac you may go a bit faster