I have a few low light easy to keep corals in my Aggressive tank with a Lion, Puffer, Tusk, Tangs, Grouper...
Most of them are just "overgrowth" from my reef but they are doing well and growing/multiplying...
Some corals like softies, can stand water that is not "pristine"
GSP, Zo's, Nepthea (tree coral), toadstool are all in my tank and doing fine..
I'm sure there are others, mushrooms would probably be OK
Just be careful how/where you place them, and you may want to run some additional actinics (which I do as a dusk/dawn light before the main lights come on)