As far as I know, if the parasites are fish parasites, then no, they cannot come in on inverts. Okay, if you want to get really technical, they could come in as free-swimming in the thin film of water that covers the inverts when you transfer them into your tank. But I don't think there have been any real tests to see if this is a significant source of parasite transfer.
However, it seems logical to assume that there are probably parasites that attack specific inverts like snails. And so you could in theory introduce invert parasites that way, but they probably do not bother fish.
sam