Yep, definitely time to stop referring to it as a 'plant.'
(though technically if it was 'cactus caulerpa' it wouldn't have been a plant either).
I am unsure of the healthy though. Mine is very similar (obviously) from the pics, and Henry's is loaded with polyp extension. However mine has been the same since I personally collected it from the Atlantic ocean myself. So who knows...
Off-topic, Henry, is that a Porites on the bottom right of your pick? How's it doing? I have a recovering piece myself that's surprising somehow doing well.