I suspect that it was a last minute idea. I too wondered if it wasn't truly his son, especially since he was marooned on that planet for 15 years and only got his wife pregnant in the last year shortly before her death. But if it were his child, I believe the notion would be that Khan was so obsessed with destroying Kirk that he not only gave up his own life in the process, but was even willing to sacrifice his young child--truly an overpowering vendetta! But I am glad it was cut.

JEDIT: Bingo beat me to it, but put it better and offered other ideas as well :)