I realize the burn-in question for IEMs may be a moot point for most informed Head-Fi-ers - that is, it doesn't happen - but it's possible that
something happens of note. My cases are anecdotal, but have been observed in both the UM2 and E4C.
I start my "burn-in" (which, of course, shouldn't exist except in my mind) by playing a CD by a Japanese trash-punk band, The Registrators. Initially, the IEM cannot handle the high levels of nearly distorted sound; it sounds like an indistinguishable mess. The volume will be barely half-way; no amping at all.
The next day, something interesting happens. The sound of the distorted music has "resolved." It's suddenly listenable and clear. No more distortion. I haven't listened in the intervening period, so my ears haven't had a chance to "adjust" to the IEM's sound yet. But using this very demanding music, something has happened to make the distortion disappear. I know these tracks like the back of my hand, so I know when they sound accurate and when they don't.
Is this burn-in? Well, assuming that burn-in doesn't happen with balanced armature IEMs, it can't be. In that case (at least in my experience), "something" happens. Call it adjustment, a fertile imagination, or "x".