Short answer: No.
Mr. Sykes keeps no inventory. He uses his FFL merely to extract a fee (exorbitant, IMO) for the transfer. Residents would still have to shop out of State and pay to have the handgun shipped to Sykes, who would hold the firearm until the D.C. registration process was complete (and he had his $125 fee).
This issue was raised in paragraph 13 of the complaint.