Our company operates both classics and NGs. Our SOPs prescribe a minimum AP engagement altitude of 1000 feet for both types, just to standardise on the lowest common denominator (being the classics). I think differentiating between the classics (certified above 1000 feet) and NGs (certified above 400 feet) would just increase the chances of inadvertent mistakes without offering any significant operational or safety benefits. We also use 1000 feet as the minimum AP engagement altitude in case of an engine failure during takeoff.
In the simulator the autopilot may slowly descend during one-engine acceleration. It shouldn't, but it does, sometimes. Especially if the engine failure occurs during a reduced thrust takeoff and the crew does not set maximum takeoff thrust on the operating engine. This might be more of a problem for the classics than the NGs, but still. However, I don't know if this simulator behaviour is realistic - never had an engine failure in real life.