It appears that ATF does not permit individuals to own the parts necessary to make a SBR or SBS prior to receiving their permission to manufacture / assemble the items. Because of this is it recommended that the same person should not purchase all of the items necessary to make a SBR or SBS and if they do, they should not take all of them home from the dealer. As a barrel can often be attached to several guns, it would be prudent to leave the barrel at your Class III dealer prior to receiving an approved ATF Form 1.
This information comes from a similar question and is found on the ATF website.
A FFL (Type-7 or Type-10) who pays the Special Occupational Tax (SOT) may possess the parts required to assemble NFA firearms (SBR or SBS). A non-licensee (individual, trust, corporation, or other business entity) or FFL who has not paid the SOT is required to register any NFA firearm via an ATF Form 1 (5320.1) prior to acquisition of the parts required to assemble such firearm.