Many planes have been painted with dope and no covering. It takes a lot of coats to seal the grain which is the primary reason I use fiberglass as an all-wood structure is normally strong enough without covering - at least the ones I build. The covering gives a nice, even base for finishing.

Also, dope is fuel-proof, but you don't have to use so much as to completely seal the grain. 3-6 good coats will make your plane plenty fuel proof, but even with 6 coats the grain will probably still show.