I would find it really skeevy if mystery guy/Henry’s father was a cop. That he hooked up with a mark, got her pregnant, got her arrested, and just left her. For me there is no coming back from that for Emma. To hook up with her just to use her to stop her from robing. It isn’t like Emma was a harden criminal or anything. She was just stealing from people which is wrong, but it isn’t like she was part of a drug ring or killing people or a gang or anything. At least that all seems wildly unlikely.
They really have to be careful, if they want the father to be a character on the show, they need to make whatever he did not be too far. Though they seem to be trying to redeem Regina which is ridiculous in light of her mass murder, cursing the whole world thing, so maybe they will make the father that skeevy and pretend that Emma would ever get over it. I hope not though.