Join Date: Dec 2014
Location: Rocky Mountains, USA
Some kinds of house wrap are designed so that water vapor can pass through in one direction but not the other, and if that's the kind you have it would certainly work, at least in theory.
Whether it would have any advantages over a paper bag or a cardboard box is at best questionable. I can't think of any.
It would certainly be more expensive, since paper bags are not hard to find pretty much for free, and the need to wrangle the wrap so it could contain turnings conveniently like a bag already can would be a hassle.
I would not be tempted to wrap green turnings tightly with house wrap or anything else.
That would be asking for mold trouble, I think.