Almost every study on human behavior contradicts this. When you have no load, your monitoring and responsiveness gets poorer, not better. (Now, you can certainly go to the other extreme and get overloaded, with the same effect).
You may have a _perception_ that you're doing better, because you feel like you're glancing around a lot, and consider that equivalent to "monitoring", but most likely you're admiring / distracted by scenery, and you wouldn't have those immediate reaction times that (remember) you're meant to have, even with Autopilot engaged.