I think with the BTA in your tank already it would be very hard to keep that and the carpet happy and carpet anemones from what I have read can very aggressive which means it will likely kill your BTA. Also they can get very big and most sites I have seen say they need a min. 30 gallon tank or larger. They are also rated as difficult to keep. I have no experience when it comes to them but I have been doing a lot of reading about nems cause I would like to get one eventually. They can be very finiky about water quality and stability. below is a link that talks a little about there needs. Also I am not sure but your lighting may not be strong enough either, everywhere seems to really say they need very intense lighting as well.
http://www.liveaquaria.com/product/prod_display.cfm?c=497+499+602&pcatid=602
also:
CarpetAnemones
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