Basically, you CAN order a short-barreled upper legally before having your Form 1 approved and back from the ATF. Most manufacturers do not demand a copy of your tax stamp (although a few do)
The reason most people prefer to "play it safe" is that having a short upper in the vicinity of a non-NFA lower could be considered "constructive intent" by the ATF, and so could technically be a crime.
The whole area is a bit unclear, since there is the additional murky question of having AR "pistol" lowers (as others have mentioned).
Once you get the Form 1 back from the ATF, an additional interesting question is whether or not to own multiple short uppers for one registered lower. I've currently got ONE registered lower, and MANY regular (non-NFA) ARs in the house. If I have two short uppers for my registered lower (one on it, and one replacement), does that somehow get into the area of constructive intent? I don't think so, but I would hate for the ATF to disagree with me.
The short answer is that unless you think you are going to be raided by the ATF, or you plan on posting picture of yourself on myspace with a regular lower and your new upper before you get the paperwork back, then there's not really any risk with getting the upper before you get the Form 1 back. However, if you want to "play it safe" and don't even want to risk some kind of technical grey legal area, then you should wait. (A clever compromise might be to just keep the upper at a different location - like work, or friends' house - until you get the Form 1 back from the ATF)