A related argument is whether or not you can ever cheer for a second MLB team.
I grew up a White Sox fan, and they're still my favorite team. But I no longer live in Chicago, and I'll be damned if I deprive myself of the pleasures of live baseball. So I've attended Nats games since I've moved here, and I feel no guilt at all about cheering for them, because 90% of the games they play are absolutely irrelevant to the White Sox. And of the ones that are relevant (interleague games), most of them involve the Nats playing a Sox AL or division rival, and therefore there's actually synergy in wanting the Nats to win.
It was different when I lived in Boston: I refused to cheer for the Red Sox, because I already had an AL team. Different league, different story.
Anyway, in a city as full of transplants as DC, and with a baseball team so relatively recent, I'd think that the Nationals fanbase would be more receptive than most to bandwagon and second-teamers.