There's no evidence to lead you to believe he is a Serial Killer who enjoys slitting children's throats. but, there is evidence that he does consider himself married and is happy with River being his wife.
This. They're both married adults, the Doctor likes her, and has apparently matured beyond "golly, gosh wow!" reaction to her from the previous two seasons. And we all know how frisky she tends to be. They're both hurting, and have plenty of time free alone together.
Unless a Sontaran in a wedding dress suddenly beams into the console room, or they're rammed by the Lusitania, I see no reason to believe there isn't a bit of hanky panky in the Tardis between now and the Christmas story.
Not sure what to think of about the Doc having children though.