I dont think they'll eat Caulerpa, but mine loves hair and film algaes. just be careful, they get big and mine is constantly moving my sand and smaller rocks around. Tons of personality makes up for it though.
as stated, they generally don't go for the macro algaes. they will consume turf and fim algaes. if the filamentous growth of hair algae is too long, they may not touch it. i find they will keep the rock mowed down if you remove the overgrowth yourself, and let them take over from there.
you should be able to harvest the caulerpa pretty easily yourself.