I'm not sure on the vagaries of building up the pistol, but I am pretty sure having a short barrel and a stock, along with a lower, upper, and all the other bits to make an SBR is considered possession of an SBR whether they are assembled or not.
This depends in part on whether there is some other use to which you could put those parts. If you possess an AR pistol, plus a rifle buffer/stock assembly, and you don't have an AR configured as a rifle, my understanding is that ATF takes the position that this amounts to "constructive possession" of an unregistered NFA firearm.
Whenever you see the word "constructive" in the law, understand that it basically means the next word is false, but that the enforcers are going to act as if it were true. "Constructive possession" doesn't necessarily have anything to do with whether or not your intend to "construct" something. ATF might similarly describe as "constructive possession" a scenario where I leave the house and my wife knows the combination to the safe where my NFA firearms are held. She isn't _actually_ in possession of those firearms, but because she has the means to possess and control them, ATF is going to act as though she actually possessed them.
Bottom line: The risk may be slight, but I would strongly encourage folks not to tempt fate by getting the requisite parts together in your possession for an NFA firearm before you have the tax stamp in hand.
Perhaps one of the lawyers 'round here can weigh in on constructive intent.
/rl