Some of the rationale of the posts here are questionable. An anemone doesn't have to be ostensibly infected to bring in an infection. The water an anemone is in can harbor pathogens. And even if the anemone is taken out of the water in the transport container before placing in the aquarium it still could transfer an infection. As for nematocysts killing ich or velvet, anemones don't get ich or velvet, but that isn't because of nematocysts. That's because those parasites target fish. Shrimp and snails and other invertebrates also don't get velvet. However, the water the anemone is in could harbor the pathogen. Experts usually suggest you quarantine everything, including live rock, for the same obvious reasons I've mentioned. So, in an ideal world, one would have a quarantine tank that is set up with all the requirements the newly purchased anemone needs (cycled, proper parameters, lighting, the whole shooting- match) and the anemone would stay there for a couple of months, and once no signs of disease are present, then it would be transferred.
I haven't done all that in the past when I was acquiring new specimens, but I was also taking a chance, as is anyone else that doesn't properly quarantine. If you are getting an anemone from an established tank where the anemone has lived for a long time disease free, then you can pretty much rest assured it is okay. Or, if you are getting a clone from a trusted source, again, you're odds are minimal of transferring a pathogen. In general, I think it is good to get your anemone(s) and then let the tank settle and not add stuff. Let what you have grow out and take good care of them, focusing your energy on keeping the water in good condition rather than experimenting with every species of animal that fascinates.