Personally, I wouldn't accept framing unless it was affixed directly to the floor underneath the carpeting. The structure will be stronger.
I think that would be as bad as installing flooring in a kitchen without removing appliances. People have done that and then can't pull the dishwasher or stove out to clean, make repairs or to even replace.
Your closet framing should be attached directly to the subfloor. For that matter, the sheetrock ceiling should be cut and removed for the top framing.
That's my opinion. My DH is a stickler for doing things right, and that's the ONLY way he would do it.
Kat