You can always try it and see, but the judge wouldn't sign the papers when my step daughter filed that way. He told her that her husband had to be there in court too because they had a child and the mother and father have to be there to decide on the child stuff.
I have heard of cases where the father's whereabouts were unknown and the mother had to have a lawyer to go through certain steps to find him or run newpaper notices and then if there was no response, the judge would grant it because measures were taken to notify him.
I also have a friend who was divorcing her husband and he was in jail at the time. He was notified of his court time but didn't arrange to have the jail take him there and for some reason they didn't make him go. The judge wouldn't grant her the divorce (they had a child too) because he didn't show up and the judge rescheduled the court date. He didn't show for that one either because immigration had already deported him and she told the judge that but he still wouldn't grant her the divorce. He said that her husband had 1 month to show for court and if he didn't that time she would have to have papers from immigration that he was deported. She got the papers and finally was granted the divorce but the judge left the child custody and stuff unsettled, giving her "temporary" custody instead of regular custody. She wanted to go back to court to try to get the custody finalized and talked with a lawyer who told her "Don't worry about it. He can't come back into the country for 10 years, so it doesn't matter." She still doesn't like the fact that she only has temporary custody but it would cost her $2000 to try to change it.
I don't know how much it costs to file papers on your own. You can try, but they may not let you.
