It's entirely possible to sustain MIs for long periods of time on pellet foods. In fact, one of the most successful Idol keepers does this exclusively. Pablo Tepoot has kept Idols for up to 5 years feeding solely NLS. Even more amazing is that the Idols didn't die in the routine "for no reason" fashion, but rather as a result of natural disaster (I believe it was a hurricane).
Paul B is right, they won't eat just any old sponge. I have heard from quite a few people who've tried that the most commonly available sponges in LFSs are not readily accepted (Tree, Fan, Ball). I have at least a dozen different sponges growing in my reef and none are even looked at twice.
There are 4 references that I could find regarding MI gut studies. The 3 most recent (1 from Japan, 2 from Hawai'i) report that MIs are found with better than 80% sponge in their guts. The last, from Gilbert Island in the 1950s (Randall) reports predominantly algal matter, but consists of only two samples.
There are no reports on size, sex, age, or anything that might even remotely indicate change in diet, but it is fairly common that those Idols that are smaller (<= 2½", 5.8cm) will more readily accept other aquarium fare. This is the point at which they're considered "post-larval juveniles". It would make a lot of sense since there can't be that much available sponge in the plankton stream, and there's so much other stuff mixed in that planktonic larvae may not be able to afford to be that "choosy".
Mine is doing so well (banner is actually growing, and now ~2.5-3x the length of the fish) that I added another yesterday. Against my better judgement, since it was not even remotely interested in food, I brought it home.
In the store, with only their tanks and other fish as background, it looked a lot larger to me. I probably should have realized that there's not much size difference between a 3+" Idol (the one I had already) and a 4" Idol (which I correctly judged this new one to be). Anyway, I guess the background threw me off because relatively, my "old one" seemed a lot smaller, at purchase, than this "new one". And he was. Much. About half the size. It's amazing what two short months in a very large tank with multiple daily feedings can do.

When I got the new one home and in the tank (after acclimation of course), I was pretty surprised at exactly how much and how quickly the existing one has grown with a more relative comparison at his side.
So, no, it didn't eat in the store. It didn't eat last night. When I introduced it, WW III broke out. The PBT, what else is new, was the first to go on the rampage, accidentally "hit" the Apolemichthys, which brought on more than the PBT could reasonably handle. Then the PBT, fleeing the Flagfin, couldn't decide which MI was which and started going for both, which brought on the rage of the Foxface who, amazingly, can pound the PBT if he gets ired up enough. The whole while, the Cleaner Wrasse is trying to clean the "new guy", who's loving every minute of the cleaning, until the PBT comes along to put an end to it. Nowhere to be seen is the almost 10" Scribbled who is still getting beat on by a 3" BG Chromis guarding its nest (spawned, again). Because the Scribbled has been getting hammered for the last few days, the Navarchus is in hiding and out of the mix as well. When things calmed down a bit, the smaller, original Idol, started picking on the new one, but in a repeated and odd way. He/she bumps/nips the new one directly in the middle of one side. This must be something of an Idol behavior I guess. The smaller one was still hanging out mostly with the Foxface last night.
This morning, I caught the new, larger Idol snatching up some Chromis eggs as the Chromis' back was turned. Not enough to sustain him, for sure, but at least a good sign that he is interested in eating something.