Is using urethane over latex paint fine?

I am trying to install chair rails at my church, attempting to match the old railing, thus I have cut the moulding on my saw using special cutters. I have as expected made gouges in the wood which are very apparent when stained. I decided to use a Tudor brown exterior latex paint on all the wood to minimize visual problems. I would like to now put a gloss urethane on the surface to come close to the original railing. Can urethane be put over the latex?