I did and they were told that's what I did, and they did not object. Obviously until it's registered, you can not use it or transport it out of your house. It's unclear how long you have to go down there and register it after taking possession. I went the next day to be safe.
I'm not a C&R, but with my first gun brought into DC back in 2008 you had to bring it in to register. This meant I drove it into DC on a Friday night, had it in my car driving from one bad jurisdiction to the wort one (and driving through a third bad one), not technically protected under FOPA, and kept it home, and then brought it down to MPD on that Monday, including though the security whihc was not well versed on what to do and shouted "gun," in response to me quietly leaning toward the cop at security and said I was transporting a secured unloaded firearm per MPD instructions.
I felt somewhat protected since I had already taken the safety course, the law course, and had an email exchange with MPD which they had told me, in writing, I had four days, although the code says 48 hours:
(a) An application for a registration certificate shall be filed (and a registration certificate issued) prior to taking possession of a firearm from a licensed dealer or from any person or organization holding a registration certificate therefor. In all other cases, an application for registration shall be filed immediately after a firearm is brought into the District. It shall be deemed compliance with the preceding sentence if such person personally communicates with the Metropolitan Police Department (as determined by the Chief to be sufficient) and provides such information as may be demanded; provided, that such person files an application for a registration certificate within 48 hours after such communication.