Tried it once in the simulator to engage the autopilot without trimming. Not nice at all, the autopilot will not necessarily disconnect, but it won't keep a straight and level path either and since it moves the trim very slowly and rudder authority is limited, chances are high you are far outside your obstacle one engine out path, or even crashed if you engaged it too early. So center the beta target, trim out the aircraft, engage the autopilot. Oh, and don't forget to aim for the correct pitch, don't sink, keep on the correct track. Not really rocket science, but nice training.
Hard to do it at home in a less complete (hardware wise) simulator environment.
Just for comparison, the 737NG can have a rudder servo, but doesn't help at all in the OEI take off case. During approach it will take over roughly around 1400 feet AGL (after the autopilot confidence test at 1500') and keep engaged throughout the rest of the flight and rollout, or go around, but will drop out once a different lateral mode is engaged. Could be similar to the 757/767 although it needs only two autopilots for that (and CAT IIIb).