Perhaps. It will greatly depend on the type of physical prize we are talking about and, of course, the person who wins it. If we go back to the Bitcointalk Community Awards from the last couple of years, we had winners who accepted the physical gifts and gave out their addresses and those who didn't. If it's an interesting item the winner wants to own, they might do it. For example, a rare BTC coin or a hardware wallet they were thinking about purchasing anyways.   

Finally, if no prizes will be paid out in bitcoin, the rules of the competition should make it clear that only users who have no problems to have the items shipped to their location can participate. So, if you don't want to, then don't play.