I was in casual platoon in 2003 to 2005 and this is what happens ( I'm assuming some things changed) Most guys there turn themselves in. If it so happens that you were caught by local police ( the Marines do put a warrant out) then the Marines send people to pick you up and bring you to MCB Quantico. There you will be processed in, usually at the MP station ( Security Battalion) and if all goes well you are sent to Casual Platoon. Now, depending on your situation two things happen a) if you really messed up while AWOL they send you to the brig for pre-trial confinement or b) they send you to Casual Platoon. Casual Platoon is pretty much like being in the fleet. You get paid and pretty much do odd jobs around base until your court martial. It took me 2 years to get my court martial. Other guys was sooner. But soon as you have it, you serve your time and then they cut you loose. Many guys get a BCD (bad conduct discharge) and if they say it follows you the rest of your life it's complete bs. The only thing it messes up is your VA benefits. Other than that you don't need to tell anyone of your military service. On my DD-214 it says BCD and then the code for court martial , other. The reason? It's extremely hard to prove desertion. The most they charge you with is AWOL.. Brig time is usually 45-60 days with I think 3 days off for good behavior per 30 days.
Now depending on your situation, you can be retained if you like or you can get out. I've seen guys do both. But if anyone says you'll get a dishonorable or you'll do like 5 years in a brig ( all stories I heard) don't let it get to you.