The only way that I can see a letter of INTENT mattering pre-waitlist is if a school thinks you won't attend - that you're using it as a safety. Hopefully, and likely, though, they will have dealt with this pre-interview, unless you said something to make it come across that way.
Otherwise, I can't see what a letter of interest adds to an already complete file. You went, you expressed enthusiasm, you wrote the secondary... some schools say, if you're on the waitlist, keep in touch. Talk to these schools frequently. Before the waitlist, though, I can't see it mattering. Were I an adcom, I would appreciate the sentiment, and probably assume that all other 3,500 applicants had the same interest but didn't feel the need to re-iterate.
I would, however, be incredibly interested to learn the value of letters of interest and letters of intent. When decisions are all in perhaps a poll of those who got in w/o communication, who got in w/ a letter of intent, letter of interest, etc. I would hypothesize that there is very little, or no significant, correlation but I'm intrigued.
