This has now been pretty definitively answered as "No". We have seen the Doctor's cot, had characters refer to him when he was "a boy". In addition, one of the results of looming is that the loomed are utterly asexual. However, given the nature of the relationship Between the Doctor and River, this is impossible. This is in keeping with the original series(where the Doctor mentioned being a boy growing up, as well as made references to his father), as well as The TV Movie, where the Doctor(where the Doctor spoke of his mother). Looms only exist in the Virgin Books line. Every other medium has made references to one or more of mothers, fathers, children, babies, growing up etc.