You could look at it that way, but he'd have to be a clone of something, another male who was identical to him in every way. Of course, if one believes that Jesus is God (I'm not sure if he is, but it's largely irrelevant to me anyway), God can do anything he wants or needs to do to get a job done. He could easily manipulate or create DNA for this particular instance.
We can run into the same thing in Hinduism with Krishna. He was born as a human male, but he is God, i.e. Vishnu incarnated. His brother Balarama is said to be an incarnation of Adi Sesha, accompanying his Lord to Earth. Maa Durga took birth as a human girl simply to deliver a message to the king who was trying to kill Krishna. When the king tried to kill her as a baby, she assumed her divine form, scared the crap out of him, then disappeared. Rama is a slightly different case, because he is Vishnu in human form, but he had a mortal mother and father. Whose DNA did Krishna and Rama have? As fully mortal men, they had to have human DNA.
The bottom line is that those of us with a particular faith would do well to not think too long and hard on things we really can't and maybe shouldn't understand. In the Lord of the Rings Gandalf told Saruman, who was deep into dabbling into the black arts, that "He that breaks a thing to find out what it is has left the path of wisdom." George Harrison said something similar in one of his songs "...the mind that wants to wander 'round the corner is an unwise mind."