Sure, that would be interesting on some level.

But I see the objective as cleaning the room, not having a clean room, so a subjective experience of being more engaged and enjoying it more is intrinsically valuable.

If it takes a lot longer or the results aren't as good, that changes things, sure, but this can be settled with a timer and a before/after photo. Controlling for degree-of-mess probably adds so much noise that this probably isn't useful in practice.