I'm an MS4 at GW and did a lot of flying for residency interviews this year and I can tell you, Dulles is not my favorite airport around here!
Your flight will probably not work out, but you can try. There is no metro (subway train) to Dulles, so you will have to take a cab and at that time of day in the DC area, it takes me over an hour with typical afternoon traffic to get to where I live which is only a little further than the airport. At some airports, getting there 40 min prior to departure will work, but at Dulles, you need to get there at least an hour beforehand because security is ridiculous and the layout of the airport is not very friendly to someone in a hurry. They have one huge security checkpoint for all the people to go thru which is a total nightmare. I seriously recommend you try to get on a later flight, especially as you may not get to walk out the door at 2:30.
Reagan National would be even better if you could switch, since the Blue line takes you from Foggy Bottom/GW to Reagan in about 30 min and the airport is well-designed enough that you could hurry to your gate without too much difficulty. They were smart enough to make several screening points, divided among the terminals, so there is usually never any one big line to hold you up. Plus no stupid shuttles to wait on to take you to detached terminals (like Dulles), as it is all in one big structure.
Anyways, good luck with interviewing! If you have any questions about GW, feel free to ask.
to those on the WL!
