star4 is absolutely right so far as tropical temperatures go. But if the gravel is being stored cold, i.e., at room temperature, the free-living stages could potentially last a lot longer.
The gold standard for leaving tanks "fallow" when trying to kill of Ick/Whitespot is to leave the aquarium without fish for two weeks. This applies equally to marine and freshwater varieties. Obviously, if you're doing this, you'll need to add a source of ammonia to keep the filter bacteria happily. Daily pinches of flake food should do the trick. In a reef tank the other organisms usually take care of this aspect, but in freshwater aquaria things are different and the plants alone won't produce the waste your filter bacteria need.
If you're in a hurry, and can't use an off-the-shelf medication for some reason, the salt/heat method is by far the safest. Despite the use of salt, this approach is actually the one favoured for sensitive fish (clown loaches, stingrays, mormyrids, etc.).
Cheers, Neale