If I stumble across a dungeon and clear it out, will this prevent any possible quests to that location? Or will the activation of a quest repopulate the dungeon?
From my experience so far, either certain areas of the dungeon will be inaccessible until you accept the quest or you will be able to complete the quest as soon as it starts by way of having already obtained whatever the dungeon holds in store. So no, you won't prevent any possible quests to that location by clearing out dungeons.
As Dave notes, some quests require you to clear dungeons or kill bosses, in which case if you've already cleared the dungeon new enemies will spawn there that you have to kill.