There is a two conductor "zip cord" with broken insulation down near the base of the compressor causing the breaker to trip. Can this connection be removed at the compressor bottom or is this connection a one piece with the compressor.

Its hard to say with the info you gave. Some compressors have a crank case heater, 2 wires very bottom of the compressor going to the heater-- with 3 wires going to mid section of the compressor to make it run. If it's the heater wires, yes it can be removed. Cap off the ends of the wires and let it fly. You can pick up a compressor heater at any local hvac supplier or company.