It is certainly possible, though it would be a longish walk. The quickest way to the Mt. Vernon Trail is to catch it on the far side of the Terminal B parking garage— see www.metwashairports.com/reagan/1187.htm . Catching the trail at the north end of the airport is somewhat more direct to where you're headed, but why spend 8 minutes walking through parking lots when you can spend 12 minutes walking down a trail? Watch out for bicyclists.

The pedestrian path goes over the westernmost span of the 14th Street Bridge (the George Mason Bridge, which carries southbound I-395 traffic).