Q: I'm wondering if it'll be a good idea to take out the whole ac compresser from my car?

The check engine light is supposed to come on if the controller detects a problem with the car that would effect the vehicle emissions. So it warns you of bad sensors, air leaks, misfires, overheating, and that sort of thing. I’m at a loss to imagine what kind of air conditioner malfunction would cause the CEL to come on. As for removing the compressor, if it is driven by a belt that doesn’t run on anything else, you may get away with it, but most cars have the AC compressor as an integral part of the belt drive and cannot work without it. Before you perform major surgery, I think you should verify that this is what you want or need to solve your problem. If you contact Your Mechanic, you can have a technician come out to your home or office to read the codes on your car and let you know what it will take to solve your problem.