Not unless you get one big enough to suck all of the air out of your house in 45 seconds flat!But seriously, by NEC, lights, fan, and receptacles can be on one circuit if it is a 20 amp circuit that ONLY serves that one bathroom and nothing else.
Otherwise, I believe you could tie into an existing general lighting circuit.
Bathrooms CAN share 1, 20 amp circuit, IF the ONLY thing that circuit powers is the receptacles in the bathrooms. Seems weird to me, but that's the code.:whistling2:
