Ummm, the short answer is "yes". The wrong answer is "no".
You can convert a pistol to a rifle and then go from that rifle back toa pistol, but not vice-versa. IOW, if you have an Ar15 pistol, you can convert it to a rifle and then back, but if you start with an AR15 rifle, you
cannot convert it to a pistol. (See
US v. Thompson Center Arms)
Make sense? Not really, but here's the logic - pistols are more restricted than long guns, under both federal law and that of most states. When you go to a gun store and purchase an AR15 registered as a pistol, you've already complied with the tighter regulations for buying and possessing a pistol If you bought an Ar15 registered as a rifle, however, and then took it home and built a pistol out of it, you could easily circumvent the tighhter restrictions on handguns.
Now, two things to keep in mind:
First, when you have it configured as a pistol, you absolutely cannot have any sort of stock or forward grip on it. With a stock, it would become an unregistered SBR, with a forward grip, it would become an unregistered AOW.
Second, the receiver must have been registered as a pistol; IOW when you did the 4473 at the gun shop, it had to be transfered as a pistol. If they transfered it to you as a rifle or a rifle receiver on the 4473, you could have a problem later on if the status of the gun becomes an issue.