Yes, I always see him along the Mount Vernon Trail (paralleling the Parkway). Once saw him having a normal conversation with a guy near Belle Haven, so think he might not be a raving homeless lunatic...just an eccentric runner.
When I saw this thread I thought, "everywhere has SOME dude that is kinda like this. I see this one guy all the time..."
Most of my running is on the trail between Old Town and the G.Mason bridge into DC, although on Sundays I'll take the trip in the other direction down to Mt. Vernon.