This seems a bit improbable as Q most likely already has the Resurrection Stone (in chapter 40, Harry relays to Q Dumbledore's description of the Resurrection Stone, and Q immediately realises that there are things he urgently has to do -- the obvious interpretation being that he has in fact seen the Stone before, not knowing what it is, and is off to get hold of it).

Though, now I think about it, perhaps that obvious interpretation is a bit too obvious and we should conclude only that Q wanted Harry to think he knew where to find the Resurrection Stone. (But there's no indication that Harry drew any such conclusion.)