Not for me. There's no correlation whatsoever as far as I can see. There are times when my hair seems not to be budging at all but my nails are looking nice, and long, and strong. Then other times my nails will not be changing in length but remain short and thin and weak/peeling while my hair appears to be doing OK.
I do think that if I'm not eating well, both suffer. But if my body is getting all the nourishment it needs, I think it's a case of survival for the fittest; so either my nails or my hair will snag the remaining nutrients and benefit. Sometimes both get lucky, sometimes either one. And then it all depends on what it is they're lacking. Since from my experience, it takes several different things in their correct proportions for my nails to respond as I'd like. I'm sure it's the same for hair.