T.S.
Be careful about creating a hero myth where here father is concerned. She's four and she doesn't know him, so honestly this really isn't about her missing her or even missing out on having a dad. This is about her thinking she is SUPPOSED to have a dad and that her's is missing.
I'd be really wary about telling her that her father is still part of your family. With all children and especially with girls, I think it's important to be clear what it looks like to be loved. If you tell her that this man loves her (and honestly you're making that up... you haven't seen or heard from him so there's no way you could KNOW that) what message are you sending about the way she should be treated by men who "love" her.
You'd do better to encourage her to love the family she has (you and her brothers). You have four people in your family. Some families have two grown ups some have one, some have one kid some have more kids some have no kids. Her her talk about her family with one grown up and three kids and let her be comfortable with that. Indulging this "daddy" thing is probably doing more harm than good.