Yes, it happens, even as the leaves are turning reddish-brown and falling off. There are a handful of autumn-blooming cherry blossoms among the thousands around the Tidal Basin, West Potomac Park, and National Mall.
You might have seen some of the Washington Post's coverage of them last year when they lasted into an unusually warm December.
The trees are at it again this year. It's not a full-throated bloom like we see in the spring, and it's relatively few trees. But they are there. Apparently they're called Higan Cherry trees (prunus subhirtella).
These shots taken this morning. If you're looking for them, these were some of the cherry trees to the west, south, and southeast of the Washington Monument.
Want to Help Support DC's Cherry Trees?
If you'd like to help support the care and upkeep of the cherry trees around the Tidal Basin, the Trust for The National Mall has launched an Endow a Cherry Tree Campaign. Donations go to the official Cherry Tree Endowment, which will give the National Park Service additional resources to fund the care, maintenance, and possible replacement of the cherry trees. You can find more information here.
The Trust is dedicated to marshaling private support for maintaining and improving the history National Mall area. I'm not affiliated with the Trust--just an admirer of their efforts.