When I turn on the a/c on my 01 CRV the engine feels like it wants to die out.

It does sound like it could be a bad a/c compressor, or an overcharged a/c system. It may be creating high pressure in the system, causing a larger load on the engine.

check the charging system and battery.

I would start by confirming the idle speed is set correctly. Your vehicle's idle should be electronically raised when the A/C is turned on. How is the idle with out the A/C on? Does the A/C blow cold while driving with the A/C on? If the A/C doesn't blow cold, I would check to A/C pressures, before condeming a A/C compressor.1997-2001 CRV's are known to have tight valve conditions. If the idle is low and rough, one of the most common problems is tight valves. If your valves are tight a series of bad things will happen. I recommend a annual valve adjustment to be on the safe side.