Cohabitating with nother woman might mess up a CALENDAR method, because cohabitating women will often find that their cycles will change to match or coincide with their roommate.
That said, it's certainly no reason why FAM wouldn't work. FAM isn't calendar or rhythm method, never has been, and never will be. It is based soley on your body's outward signs - CM, temperature, and cervical position - that won't change just because your body is trying to shift to a different cycle pattern. We all have the same hormones released at the same relative times in relation to our own cycle, and those will usually give reliable signals to tell you when you are fertile or not.