I'm almost sure he would! That of course the problem with privilege especially theirs, is that it does have a downside. However much you might want to go to, belong to, or have as a career, you simply can't! You can only do things that are mapped out for you, bit like being in a guilded cage which must be frustrating particularly for modern young people. Money and position for certain is a two edged sword. That's why William and Katherine so enjoyed living in Wales, for a short time they could be a bit more normal.
It's been interesting reading the posts of people's military relatives as they reflect my own. My OH was in the Fleet Air Arm, joining as a boy sailor, in search and rescue, leaving the Navy some twelve years later with the rank of Sub Lieutenant, not a particularly high rank, but respectable for an 11+ failure! My own father joined the RAFVR in 1940 as an Aircraftsman, before losing his life in Dec 1942 with the rank of Flying Officer. Coming from a working class background, he did go to Grammar School, so no doubt that helped. Other family members were also in the forces during both world wars. I can't see that a President would have the same interest world wide as the immediate members of the royal family, and certainly wouldn't draw the crowds or the money those crowds generate.