Yes you *can* use distilled water for your reef aquarium. All the elements are introduced into the water via the salt mix, so there's no problem with "having it strip everything"
The one downside is that distilled is very resource intensive to produce so its over kill for a reef. Try and calculate how much water you will be using, for the initial fill up regular water changes evaporation Try and determine if your distiller can keep up with that, if not it would be in your overall interest to use a conventional RO/DI unit (simply because it takes so long to produce distilled water) Robert