Will Teflon tape seal the nylon drain plug adequately or do I need some kind of pipe dope?
I always use 2.5 wraps of teflon tape. As with any tape application make sure that the tape does not go all the way to the end of the threads-- you don't want any breaking off in the water heater.
Replace the nylon Atwood plug annually.
If the plug breaks when trying to remove it, the sprinkler head remover from any box store works well.
And I would add, do NOT be tempted to use a metal plug. I have run across plugs made of brass, steel, and some kind of pot metal. A metal plug will be subject to electrolysis due to dissimilar metals, and can "weld" itself to the aluminum water tank threads, making it very difficult to remove.
Gave up on relying on Teflon tape for thread seal, long ago. Like to use Permatex Thread Sealant tube, which is what we used on nylon drain plug for our twice a year hot water tank flush. Always have a spare nylon drain plug.
I used a brass plug with pipe dope then I found that the white plastic pipe plugs work without dope or tape. Later I canned the plug idea altogether and went with an electric heating element.
FWIW, If you use tape, a good quality PTFE tape is Blue Monster™ PTFE Thread Seal Tape (https://cleanfit.com/blue_monster_ptfe_thread_seal_tape_70885.shtml) and for most, one role will last a long time.
I had always used those small roles of white tape in the blue sided dispenser you see everywhere, but they seem to have been cost optimized (pre-stretched and extra thin). I've seen the above at HD, I got mine at a plumbing supply store. It was the plumber who installed our hot water heater who turned me on to this brand.
Agree with Steve to only use high quality branded thicker Teflon tape. Never use blue/white generic. For similar reasons, we also only use Scotch Super 88 electrical tape which is .008", thicker than all others. We never use generic electric tape. Also never pull Teflon or electric tape like many do, to disconnect a piece from the roll. We cut with scissors.