No, if that were the case, I would be overrun with them in my 39 year old tank.
I know that is the thinking but I have not found that to be the case.
I have about 20 of them but only because I am too lazy to stick my hands in there to kill all of them. Some of them are in places where I would have to move rocks to get to them and they don't bother me so I leave them there.
I kind of like a few of them as long as they remain a few. After all, they are anemones which are a normal part of the sea, we just choose to kill them because we like other stuff better. Years ago we actually tried to keep these things alive and paid more for rocks with mojanos on them. Yes I know, wierd.