Can signed court documents by both parties and notary hold up in court?

Long story short, I was married on 9/13/14 and it ended on 9/23/14. I was 2 months pregnant and scared so I got married. It ended faster than it began. He was never in the picture and only met my daughter once, 3 days after she was born for 30 minutes and that was the last we saw of him. I didn't file for divorce, legal custody, or child support because all of my money went to my daughter since I am a full time single parent. She is now 19 months. I am not interested in child support. I just want my divorce and legal full and sole custody. Basically everything I have now but legalized. If the other party is willing to sign divorce papers and custody papers, can I have someone serve him, sign on the spot, along with a notary there? Would I be able to bring the papers to the court house and have them filed or give them to a judge?