[SmokeRulz]

First off, to clarify, the Cleric's Resurrection ability doesn't HAVE to be used specifically on the Kick Down the Door phase. It can be used at any point you'd draw a face-up card(s). You also aren't actually skipping the door kicking, you're just replacing the door you would have drawn with the top discard instead. So don't get too confused there.

As for your actual question, assuming Divine Intervention is the card on top of the discard, yes you could Resurrect it and gain its effects. The Clerics that come after you could also do so, but only if Divine Intervention is still on top of the discards at that point. If you discard anything else to the Door deck during your turn after using Divine, then it will get covered up.

Wait for an official ruling on this one, of course. It's possible that because of Divine Intervention's immediate effect, your discard cost may come afterward, which would cover the card up right after using it, so the next two Clerics wouldn't be able to resurrect it.