I can't say for sure, I decided I wanted to keep angels and didn't mind what they ate. I have a 4 head hammer coral and mine doesn't even look at it.
Picking may or may not be a problem for your coral. If it is a fast grower I wouldn't worry that much, unless of course the angel continuously picks it to death. My angel picks at my 1 kenya tree all the time and it still grows like crazy.
You could try the angel, and if he tries picking at it too much then try moving that coral to a higher location in the tank, or a location the angel doesn't swim very much. IMO my angel only eats corals at the bottom of the tank, and ones near his cave.