I would never trust any angel with acans or any other fleshy brain-type LPS. As LargeAngles says, they are very nearly irresistible to angels. People have reported having better success with more noxious LPS like frogspawn, hammers, and galaxy corals.
Other angels like soft corals such as zoanthids, mushrooms, ricordeas, xenia, anthelia, etc., but will leave sinularia and other softies alone.
As to SPS, it's also something of a crapshoot. A multibar angel that never picked at sps in the tank of the guy I got him from chomped a pocilipora frag I had within two minutes of putting it in my tank. He's largely left my montis alone.
In other words, it depends on the fish and it's hard to predict.