If you moved in together, would you be supporting them, or would the mother be working? If she was covering 100% of the children's expenses (whether from CS from the bio father, her income, or both) that weighs in your favour.
Would the children see you as a step-dad? How much would you involve yourself in their lives? Would you take them to and from school, get involved in their sports or other activities, go to parent/teacher meetings? Would you care for them when they home sick from school? Would you introduce them to your own family and would the be treated as family by your parents etc? These questions would all come into play.
There is no black and white answer, it would be a combination of things. If you tended to keep them at arm's length (but certainly be friendly and caring) and have the mother take care of all expenses, organize all activities and take care of discipline, etc that would put you as less of a parental figure. They also probably wouldn't like you very much.
Personally I would look at this situation as, do I want a family and would I otherwise be willing to adopt them? I'm speaking somewhat from experience here, I dated a woman with a child many years ago, before I was married, and these things all went through my head at the time. When our relationship ended I would have actually been very willing to pay support for the child, I cared for her very much. But not everyone is going to feel the same way and that doesn't reflect on you if you don't, it should be a choice. However don't try to sit on the fence, don't try to be a stepparent and then deny it after the relationship sours.