As someone on the other side of the process - i.e. I have been involved in the interviews of many candidates - I wouldn't recommend a follow-up letter, unless you're providing new information additional to what had been discussed in the interview. For example, if you were asked a question and were unsure of the answer but offered to get back to the interviewer later with more information. (In such a case, we probably would be looking out to see whether you followed up or not!)
You will have thanked them for their time etc in person, at the interview, so I don't see the point of a follow-up e-mail saying the same thing. When we receive them, we certainly do read them and put them on the candidate's file, but it seems very obvious that they're only doing it out of perceived interview etiquette. To me, I find it a little smarmy - and, particularly with MCNs, I don't think it would sway anyone's decision one way or the other.
Do bear in mind that, even if there's a delay in getting back to you, it quite often isn't a case that you didn't get the job - there's just been hold-ups behind the scenes, where the company are agreeing on the terms of the offer, etc. We are well aware of how nerve-wracking the wait can be for candidates, and always try to let successful candidates know as soon as possible - unavoidable delays do sometimes happen, though.
What I might suggest is, once a couple of weeks have passed and you're quite sure that you didn't get the job, you could send a letter/e-mail. Thank them again for their time, and ask whether they might be able to provide you with any feedback from the interview. Also, reiterate your interest in the company (not the role), being as specific as possible about what attracts you to this company, and mention that you would be very interested in any similar opportunities which may arise within the company in the future. At this stage, you have nothing to lose. And, if you were a close No. 2 candidate for the job, a follow-up will end things on good terms - and may put you at the top of the list of potential candidates, next time a position comes up.
Best of luck!