Is a DSB in a 12-gallon reef tank feasible?

Hello all! I am putting together a reef setup in a 12-gallon NanoCube, and was wondering it a DSB would be helpful in controlling nitrates. I am getting the tank pre-cycled, with some rock, water, and sand. I was thinking of adding 20 or so lb to the 10-20 that is already in it. I know DSB are very effective in large tanks, but would one in this size of tank work?

I'll start a poll, so if you could drop a vote it would be really appreciated! I would also appreciate additional feedback.

Another thing I was considering would be to remove the old sand, and replace it with 30-40 lb of black sand. Would this affect the tank in terms of it being cycled? The tank also comes with a few fish, and I'm wondering if they will be okay if I do this. I appreciate any help!!!