It will take a little while, there is no guarantee that it will host the anemone though.
and yes the BTA also get large, the sebae are even larger than the BTA though. The BTA usually splits when it gets very large as well so you could take one half back to the LFS
Did you get the anemone specifically for the clown to host it? If not you could look into getting the flower/rock anemone, they stay small and tend not to move a lot so it would be a better choice for a nano. Another option would be the mini maxi carpet anemone, they come in a variety of colors and also stay small and don't move around a lot.