This is about to change as the United States is allowing ICANN to go its own way in some matters. While the details are not entirely clear, what is assumed is that ICANN will still be recognized by everyone as the internet arbitration body for the sake of smooth transition. What will change; however, is that other countries will use this to gain sway over ICANN and make it more of an international body.
There are pros and cons to this probability. What concerns me are the cons. The major con is that most countries are not free. While giving Ireland more say would not be a problem, for every Ireland there is several Cubas, Sudans, People's Republic of Chinas, and Russia. The in vogue thing right now for governments to shut down critical presses like in Venezuela and, unfortunately, Honduras. Giving say or control of their own domains to these dictatorships will only harm freedom and peace worldwide.