If a set of AC compressors were wired incorrectly, is it possible the units could run for several months and then fail completely.

Wiring to a compressor needs to be done correctly. Voltage needs to match the requirement of the nameplate. Furthermore, is the unit single- or three-phase? Voltages will vary if the building electrical service is single- or three-phase. Generally, single-phase will be 230-240 volts. Three-phase transformer connections can be 208 volts phase-to-phase (wye connected) or 240 volts phase-to-phase (delta connected), or higher (generally 480 volts). This is important because if the voltage is too low the compressor(s) will draw more current to do the same amount of work (power is the constant required to do the work (voltage x current)). This results in overheating of windings and wiring. In certain instances, the current drawn may exceed fuse or circuit breaker ratings, causing blown fuses or tripped breakers. While not generally required for compressor or fan motor operation, it is also important to have a properly sized ground wire run to the compressor(s) for safety. If an ungrounded compressor were to develop a shorted winding it could present a life-threatening electrocution hazard. A properly grounded compressor would trip the circuit breaker or blow the fuse if it developed a short to the case.

To more definitively answer your question: Yes, it is possible for the compressors to operate for some period before failing.

I hope this answers your question.