From what i've seen at the LFS i work at, fiddlers can't usually catch fish to eat. They're pretty slow. Not to say that if they did have a chance they wouldn't take it. Slight risk, but not too bad. I would say 80%+ chance that they would be fine with the BB goby.
As far as brackish tanks go you woud definately want a larger tank. Especially if you want some of the more common (and in my opinion, "cooler") brackish species. IE; archers, scats, monos. In the next few months i plan on setting up a 65 gallon brackish tank.
As stated earlier, you could do a 20L with a few mudskippers, and fiddlers. The skippers may eat the tiny BB gobies though.
1 10 gal low tech planted tank. 1- 10 gal lowtech w/ diy co2. 55 gal lowtech planted tank. 20 gallon reef tank. 55 gallon paludarium for dart frogs. large exo-terra vivarium for madagascar giant day gecko. working on getting 65 gal brackish tank soon