Is the absent father better dead or alive?

In your situation I feel you absolutely are warranted since he does not claim your daughter. I will say I grew up same way. My father did not choose to be within my life whatsoever. He told me once I had gotten old enough to understand that he basically could only be a friend to me and we've probably only spoken five times in the last 12 years. I haven't seen him in 12 years and he beat me before that whenever I was with him. I wish my mother never lied to me about him loving me because I believed her, you're making a great decision

I wouldn't, here's my reasoning:
1) It doesn't save her the hurt its just a different kind of hurt, swapping abandonment for the grief of a father.
2) You run the risk of having her start to idolize her father's spirit as she grows, she is going to fill in the blanks about who he would be if he was still alive with things she would hope for.
3) You'll still need to explain why his family is not in her life.
4) She will find out eventually, either through curiosity or accidentally when filling out government forms, fafsa for example if she wants to go to college one day would flag her if she put her father down as deceased when he wasn't. Death records are public.

If I were you I would tell her the truth in a way thats appropriate for a child to hear. When I was little my mom would tell me I didn't have a father just a mom, and did so until I was 6 or so and we could talk about it. That and teach her that her value doesn't depend on other peoples proximity to her, people move freely in and out of our lives