He was born of Mary, and in the Bible there's a genealogy that traces Mary to David off of her family tree.
Joseph was one of Solomon's descendants, while Mary was a descendant of one of David's other children.
So in a sense, yes. Also, no. It's really a difficult question.
The first reason I have for saying that he is not the son of Joseph by his seed is that he is an entirely fictional character created by the bible with only very exaggerated and biased proof of his existing at all. My second reason for saying no is that he isn't in the bible. Even though Mary and Joseph were related, he did not drop any semen in her. His seed was not involved.
Mary was a virgin, and Jesus was conceived before she married Joseph, and she was still a virgin, so Jesus is not born of Joseph's seed. That's all I have to say on this matter, I don't really care if people say I'm wrong or right, It's my own opinion.