Is it possible to add a DSB to an established FO tank that has a matured wet dry, or does the wet dry have the same effect on the DSB as it would on live rock(competing for nutrients)?
No, with a DSB you set up a anoxic zone(a low O2 zone) that allows a bacteria(I've forgotten the name off hand) that will break down nitrates, a process that does not occur in your wet/dry. So you can run them both, the DSB will essentiall be a denirtification filter, which in a FO tank may not be that neccessary, as long as you do normal water changes and skim the water.
Anaerobic bacteria are what you are referring to, and you don't need to skim a FO tank if you do regular water changes. Especially if you maintain the hardier species - hell I kept FO tanks with great success for years before I know what a skimmer was. It's not a bad idea to run one though...delicate species will apprecaite it.