as long as you keep the caulerpa pruned, it's fine. i've been using a mix of macroalgae including various types of caulerpa for 5 years without issue.
as for a plant "going asexual", i'm not sure that's the right term.
wikipedia says: Asexuality (also known asnonsexuality[1]) in its broadest sense, describes lack of sexual attraction,[2][3] or interest in or desire for sex.[4] Sometimes, it is considered a lack of a sexual orientation