I believe the only thing an invert can pass on to a fish will be whatever is hitchiking in whatever water comes over. The parasite will be in the drops of water on the invert.
If you do quarantine your inverts, then to do it right, you're going to have to leave them in the QT for at least 8 weeks. That's the "fishless" time that ich needs before it supposedly will be killed off. Any shorter period and you can still have ich in your water.
When I started this hobby, I had every intention of quarantining everything. But once I thought through the 8 week quarantine, I realized that with my initial cleanup crew, many would have starved because there just wouldn't have been enough to eat in my 10g QT over a 8-week period.
I do quarantine fish though - minimum of 4 weeks.