I checked out the flying club's website, it didn't seem that they had T-34s listed under their aircraft section. That and the field is 45 minutes plus from Quantico. If they do have T-34s it'd be worth the drive though.
They did when I was there. Just give them a call or shoot an email to one of the contacts.
You might want to check around for a mid that is checked out in their T-34's to split the time with rather than paying an instructor. You could ask DanMav or someone thats there right now to post a bulletin on the LAN to find someone. Hit up the Bay Bridge Airport or Easton for a hundred dollar hamburger. You see alot of cool things fly in to Easton, L-39's, Migs, and such. Have fun and stay safe.
) . The Navy club did allow active duty members last time I was down there which has been at least three years.