They can, even though they are usually unlikely to get it.
If all your old fish died I would wonder if it really was ich or something more lethal.
It could also be that the tank has a serious issue.
So I wouldn't add any new fish until you can be sure the tank is OK and most dangerous parasites have died out.
Two months without fish will eliminate Amyloodinium, Brooklynella and possibly even Cryptocaryon.