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.