I believe they will starve, but they are cheap. They end up as food in my tank. Not all nudibrach eat aptaisia, so watch what you buy.
The peppermint work in my over flow and sump. They end up as food in my tank...Haha Haha lots of things end up as good in my tank.
Like most of the animal remediation, if they are not hungry they may not eat it.
There is a great video from bulk reef supply..20 common mistakes for aptaisia. Definatly worth finding.
So most likely it is always in your tank. It will take over if you don't respond quickly and constantly.
So I use aptasia x...which can cause it to spread, file fish, copper band and peppermint shrimp and I have something in all parts of my tank, overflow, sump, and dt I have lost too many fish to aptasia stings.
I like the berghia, but again they are good in my tank