Absolutely not. As others pointed out a thank you letter is just that - a thank you letter, which should be short, crisp and clear. What I have found works for me is to ask this question as one of the last ones at the end of an interview. This is me - "Thank you for your time. I really enjoyed our conversation about this opportunity. Before we end I want to let you know I am very interested in the position and want to make sure you have everything you need to help make a decision. Therefore, is there anything else you need to know about me that did not come up during our interview?" I found that this question shows them I am interested, willing to provide more info to help them and depending on their response you are in effect getting some interview feedback that you don't want to ask for with your thank you letter. Hope this helps and good luck with your search.

Send a letter thanking for the interview

Hi Lance, Use the Thank You letter only to thank the interviewer. You can feel free to follow up at a later date to ask for feedback, but please understand that most interviewers are not comfortable giving constructive criticism, so you may not get the information you're looking for.
Thanks for the great question! Marijoy

Use the thank you letter for it's main purpose. Requesting feedback before they decide on a candidate might be a deal breaker.