So I can just replace ac compressor an bypass heater core an ac should work for 1991 Lincoln Town car

If the compressor is the problem A/C should work. But I work with idiots. I replace the compressor, expansion valve and dryer. And clean the system out. They replaced the compressor. then the expansion valve. then did it again after they clean the lines out, Then again, because the dryer held to much metal from the compressor going bad. And yes, you can bypass the heater core. But if the blend door actuator is bad, it won't be cold.