I think a test run is a good idea. Whether you can get through Fort Belvior is unknown -- I'd suggest calling them. I used to commute through Fort Meyer, and all they required was a Government ID, which I had. Right before 9/11, they were getting ready to require a special permit to travel through their facility.
Since my post-9/11 route does not use the fort, I never found out whether or not the plan to issue a free permit was carrried out or whether everyone is banned from the fort.
Fort Meyer has beautiful 19th century military architecture. I miss riding through there -- and the gate guards were always polite and friendly.
I hope your commute is pleasant and practical for you. If I didn't commute, I wouldn't ride at all -- or get any other significant excercise.
Have a good ride --
Paul