I've seen them do this at the LFS and the clowns looked unaffected, though this was a tank of about 15 clowns and 3 or 4 anemones, so I'm sure the anemones weren't too happy with that many critters crawling all over them. Doubly so since the clowns ducked for cover every single time someone walked by the tank, so normal, I'd say yeah, but I don't know what affect it would have on an anemone.
-Al