[Edited:] My advice would be not to pronounce the h after an. This what I have always heard style books recommend.
I assumed that most people, if not all, who use an did not pronounce the h. I certainly can't remember ever hearing h pronounced after an; but it is always very dangerous to predict whether something is always or never the case. Wait, let me rephrase that: it is nearly always very dangerous... The main cause of this danger is that there will nearly always (see, I am learning) be exceptions. Even so, I believe they are exceptions; if someone disagrees and provides a decent argument or evidence, I will edit this answer again.
The use of a versus an in English is almost entirely based on whether the next word is pronounced as a vowel or not. The way it is spelled usually does not matter; compare a user, an honour. Based on this pattern, the advice of style books, and what I suspect is the pronunciation of a large majority, pronouncing the h with an seems like a bad idea. The fact that some people on this very page and elsewhere perceive it as "affected", and that it will displease traditionalists, would seem reason enough to drop either the h or an. A traditionalist might think, "hey, that guy is trying to sound cool, but he fails miserably, because he doesn't quite understand how it works", even if the speaker did in fact understand, but simply made a different choice. Such is snobbery.