You're absolutley correct - they will. Small feather dusters as well.
I'm not a fan of the copperband because of it's high mortality rate and sensitivity in small tanks. A good fish in a larger tank, and once acclimated fairly hardy like most butterflies, but a fish I really wish fish stores would leave in the ocean simply because they suffer very high mortality rates. IMHO -
I've had Aiptasia big enough to charge rent, and they sting. If they wouldn't spread like dandelions the bigger ones are actually kind of pretty. My coral banded shrimp will steal food from any anemone, but leaves the aptasia alone because it's obvious they nail him hard when he touches them.
In one case got a piece of live rock so badly infested with the stuff I decided to cook it. Bad, BAD idea. You have no idea how bad that smelled. The odor could have knocked a buzzard off an out-house. Gawd that smell was awfull.
Aiptasia doesn't thrive in tanks with a lot of other competition as I've learned. In the one other tank I had with aiptasia brought in with 'bad rock', the pests died off after I went full reef with it. Aiptasia doesn't seem to like a typical reef tank with elevated PH and alk, and /or aggresive skimming, and just withered away.