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If you put anything from an invented tank into your display you are more than likely introducing ich into your tank. An anemone or any other invert cannot host the parasite, but at any point the parasite can be free swimming in water. So just by introducing the water you can infect your tank. You can qt your new arrivals and be sure not to infect your display
if you put wet live rock into you tank from an infested tank, you could introduce it into yours, it may only be a few free swimming parasite that came up with the LR, but once in your tank and they find a host, they will be off to the races.