I did this. My ex was a truck driver, and moved around all the time. He dropped out of contact with us for a couple of years, and I persued a divorce finally about 4 years after he left. I used a paralegal (one of those places that advertise a $99 will, $99 bankruptcy filing, etc) and it cost me about $150 plus some newspaper ad fees and filing fees... at most $200. I don't know how they do it state by state, but it was very very easy...easier even than divorcing him if he was around. I just had to make a "true effort" to find him, I did an internet search and when that did not work I had to post something in the local newspaper (he wasnt living there, I knew that much, but that was all they required) and he had x amt of time to respond. When he did not, I was able to divorce him, get full custody, and get on with my life. Submitting all the paperwork was a little bit daunting, but between the divorce department at the courthouse, the courthouse's online walkthrough, and the paralegal I managed to wade through it without much trouble. (think I had to resubmit a couple of things that I did wrong, but the courthouse had no problem letting me know where I screwed up, lol)
There was no arguing in court, no debates, no need for a lawyer in my case. I walked into the courthouse about 6 months after I filed (had to give him ample time to respond for every step in the case) and the judge granted me everything I asked for with a stipulation that he was welcome to take me to court if he ever wanted to contest it (which was basically everything that I already had... our home, everything on the premesis, full custody, no alimony, etc).
In my case, the amusing thing is that he sent a legal courier to my parents house about 3 yrs later (after I was happily remarried) attempting to bring me to court to divorce me. I guess he had found a new sucker to marry him.