Probably not. Under Jewish law, a man who took a Nazirite vow would grow his hair long as a sign he was under a vow (Numbers 6:5). Consequently, it is most likely that every man not under a Nazirite vow would have short hair, otherwise the long hair of a Nazirite would not mean anything. We know Jesus was not a Nazirite as he drank wine and touched dead bodies (Numbers 6:3,6).
Sometimes 1 Corinthians 11:14 is used to argue that Jesus could not have had long hair. However, that is not so relevant as it deals with the practices in Corinth which were very different from those in Judea and Galilee.