[Zfdeisde]

So if I simply hit another ball without declaring it a provisional, this would be my third stroke and the other ball would be dead and no one could look for it?

Your 2nd ball, without the declaration of it being a provisional, is not a ball in play under the Rules. Technically, it would not count as a stroke at all and you'd either have to walk back to the tee and declare that you were hitting a provisional ball under stroke and distance (your 3rd stroke) or take a 2 stroke penalty and drop a ball in play near where you thought your original ball was (lying 3, hitting 4).