Yes I think it does.
I was looking at pictures from a couple of years ago and my skin looked really good and my hair looked long (MBl though very thin due to too muchflat ironing). At this time, I used to work retail and I remember I would have customers come up to me all the time and tell me how beautiful my complexion was (mostly older white women and men which I found interesting). I believe this was due to the fact that I ate really healthy (I ate mostly lean meats like turkey, chicken, fish, eggs, consumed limited amounts of processed foods, alcohol, and carbs). I also drank tons of water, daily protein shakes from Odwalla and Naked, and stayed physically active by walking a lot throughout the day. My skin and hair seemed to flourish though I took no multivitamins and did no protective styles. Had I done protective styles though I belive my hair would have been much thicker and retained even more growth.
However once I got a desk job, stopped getting daily exercise, eating junk food, and drinking alcohol frequently it seemed like my hair growth slowed for sure. My skin also started breaking out more.
My hair growth didn't really pick back up until recently when I started taking multivitamins.
However it seemed to be really good back when I had a good diet, walked alot, and drank lots of water. Diet definitely plays a role. Particularly if you consume processed foods, alcohol, and caffeine. Your body has to use essential vitamins and nutrients that may be useful for hair to rid itself of artificial ingredients, presertatives, and toxins from consuming these types of things.
I believe that is why when I graduated college and moved back home for a while, I lost so much weight. I lost between 15-20 pounds (I went from 145 pounds to 128 pounds. I am 5'8 so 128 pounds looked really good on me) from eliminating processed foods and fast food from my diet. My hair and skin improved immediately as well.
For some people diet doesn't play a role but for most it does.