Being peacocked is a truely important part of your game, not just hairstyle, but cloths aswel, wear unusual cloths, if you have an unusual hairstyle, they go hand in hand with each other.
So as an answer, yes, hairstyle is important, go to a hairdressers near you and tell them you want something different, that you want to stand out, hear what ideas they got and then roll with one of them!
It isn't as important as other parts of game. I don't use peacocking at all and I have gr8 results, regular fc, ltrs, nice chicks. I know what to do to have even better and it isn't, because of peacocking.
It depends on your game, if you need openers etc. peacocking can help, but still I'm sure that inner game is the most important.