Sure it holds. The President has control over a certain geographical territory and people born in that territory. Now, some people recognize his authority over that territory and those people, others don't. Some people obey laws that he brings into existence concerning that territory and those people, others don't. Some people think he's a legitimate president, others don't. But personal opinion, the ability to be caught and brought before a judge, the willingness to prosecute people who are treasonous towards the President, these things don't change the facts. Bush is President.
Just change the word Pope for President and you've got nearly the same thing, except the Pope has authority over all the baptized. Whether the baptized choose to recognize that, whether anyone requires them to make that recognition - none of that is relevant to the facts.
You must be coming from a Roman Catholic belief system, which some of us as Protestants do not subscribe to because it is often not biblical.
Your analogy does not work. People can accept the Pope as the head of the RCC and admit that he is the legitimate head of that denomination. However, at the same time, they can also belong to a denomination that does not accept the Pope as its head. Orthodoxy, for example.
Similarly, people can recognize that GWB is the legitimate President of the USA while, at the same time, living in a country that does not recognize him as their head of state. The United Kingdom, for example.