I know this isn't answering your question, as I haven't done it.
IMHO,
If you plan on keeping the gun from now on, it would probably be ok.
However,
To have just a semi-auto .22 and spending $200, also marking the receiver with your name and address, plus the wait till the forms come back is a bit much to invest in a 15-22..
I think if I were to SBR a AR15 type rifle, it would be a Colt or any standard AR, that way, you could put on a DOE (7 inch barreled upper) in 9mm, or a Colt 635 (10 1/2" upper) in 9mm, put any length .223 barrel on it, also put a deducated .22 barrel in any length you desire on it. It would be much more flexible and desirable to do.
If it were me, and funds weren't an issue, I'd just opt. for a M16 and be done with it.
Good luck with your decision.
augy