Short answer is yes. Once you have the approved form1 with the tax stamp all that's left is shortening and threading.
In the case of a 10-22, you may do better buying a threaded shorty barrel. Lot's of outfits sell them online. Since Ruger introduced the Charger there is a market for pistol length 10-22 barrels. Lots of guys with silencers want to put it on their Charger (or 10-22 SBR, it's a popular rifle to SBR), so the demand is filled by outfits selling suppressor ready short barrels. You may find that getting your barrel shortened and threaded may or may not be cheaper than buying one ready to screw on. Also, keeping the regular barrel on hand may be a good idea. Once the receiver is regisatered as an SBR, it's a registered SBR irregardless of what barrel is on it. In the case of a gun who's barrel is so readily interchangeable it's not against the law if you want to put the original barrel back on for an afternoon's 'regular' rifle plinking, then put the shorty back on later. With a design as modular as the 10-22, why not have a couple of different barrels and stocks.
Do a little searching online and see what's out there. You obviously can't buy the barrel 'till your form comes back but there is certainly no law against drooling at catalogs while you wait for the wheels of the beurocracy to do their thing.
Oh yeah. When you fill out the form, the over all length (in the federal guidelines) of a rifle with a folding stock refers to the length when opened. You can paper it with the original non-folder and then put a folder on later. As I understand it that doesn't become a 'permanent change' that requires written notice. I'm 99% sure about that, so double check it.
