I know this is a little late, and hopefully you've had the opportunity to go and check it out for yourself by now, but just my .02 for one trip. I went up there for a day hike and got to check out a few of the bike trails. Most of the roads are pretty gravelly and some stretches of decently packed dirt. I probably wouldn't take a road out there but an MTB would be a blast. Some spots are decently hilly so at least it can be a bit of a workout depending on the route. There's also quite a bit of distance available if you're looking for it. I believe I read something like 100 miles of total road (both gravel and dirt).
I've actually riddin there many times both on mtb and on my road bike. The rb climbs are good training and you can put a lot of miles in riding the dirt roads. Just watch out for the soft sand that will drop you quickly if you dont spot it in time.
Also, there is little to no phone service on parts of the refuge so let someone know where you will be. Best thing about it is the solitude.