I have to disagree, for a couple reasons. First, this equates Starfleet with a given branch of the U.S. military. While Starfleet is the "military" spacefleet of the Federation, it really serves a huge number of purposes that most people wouldn't associate with, say, the Navy; alongside things one would expect, such as defense, escort, some spying, and so forth, Starfleet is also intimately involved in exploration and mapping, diplomacy, and so forth. I've always assummed that Starfleet was much more real and significant in the lives of Federation civilians than the military (plus, remember, it's representing the entire Federation, not just the United States).
But, there are plenty of statements throughout TNG that suggest that Picard is something of a Federation celebrity beyond comparison with any contemporary military admiral; and, most of the TNG books I've read (and, yes, I know it's not "canon") also suggest that Picard is quite famous.
And, if you think about it, who would the potential competitors be? Planetary governors, who wouldn't be that famous outside of their home system? Other people in Starfleet? In the 24th century, Picard would probably be quite famous, and his eloquence and charisma would almost assuredly make him a lock, if he ran.
