Technically you should be able to take the upper with you but the registered lower would have to stay at the dealer until your stamp arrives. You can't put a brace on the lower once it's registered as a SBR (short barreled rifle). Once it's a rifle it can't be a pistol ever again whether it was built as a rifle or you converted it to a rifle after your stamp came in. There are some grey areas if you're willing to risk the ATF thing but that's my understanding on the pistol/rifle/SBR stuff.
I quit registering for SBRs once I got tired of dealing with the forms for travelling out of state. Yes, you can submit in bulk and get approved for a year at a time per SBR but it's just a PITA and I don't need the ATF or any other agency knowing when or where I'm going. I just build pistols now that the braces are pretty much as good as a stock.
Why not just take a non sbr rifle with you?