That would, aside from being completely impossible in various ways, actually answer a few questions. Such as how the Defense Professor (don't want to assign him an actual name when talking about who he might be) is able to do intricate and powerful magic in any body he wears. It would be, to use his word, inefficient to just be that powerful and that in control of his magic. We already know, from Tonks-as-Susan, that a Metamorphmagus can do amazing magic while Metamorphed (probably because they have no "natural" form and are equally comfortable with any humanoid body); this makes it likely that the Defense Professor is a Metamorphmagus somehow. Of course, that doesn't explain why he needs to "rest", which other theories do, so we'd need both this and a completely separate explanation of the resting, which are less probably by conjunction.

Also, on an out-of-world note, I doubt Eliezer Yudkowsky would have made the particular comment above if the Defense Professor were a Metamorphmagus; he would be more likely to say Sprout, McGonagall, or Hannah Abbott.