Generally, yes. Even with obeying all traffic regulations, I was able to go from the Waterfront area to Columbia Heights in about 30 minutes, without breaking too much of a sweat. And that included stops to take photos along the way.
This is the route that I took today. The "end" sign is where I stopped to dock the bike at 5th and K and take photos.
As long as you return your bike to a docking station, rather than locking it up elsewhere while you run an errand, I don't think that keeping within the 30 minute timeframe should be a problem at all. Even if you take up to an hour to get somewhere, its just a $1.50. That's a total of $6.50 for a single one-hour trip if you purchase a day-membership ($5 membership fee plus $1.50 trip fee). How much would it cost to take a cab for an hour? A heck of a lot more. And given the choice between walking 10 blocks from a metro stop to my destination, and riding 10 blocks, I'd take the ride.
Do you think the bikeshare program is affordable and convenient?