Hard to say for sure if the police will believe you or your son. My guess is that they will review the situation for themselves once there.
You can tell them verbatim what your son has said and they will make their own determination. Don't worry what he says about you or what the neighbors think. Just make the call and remain as unemotional as possible...explaining the facts. Also, if he writes a suicide note again, quietly print it out and of course, make the call!
You might offer him a reasonable incentive to on his own study and take the GED. Not sure what that would be, but I wouldn't go overboard. The truth is that he should want to take care of that on his own. If you do something like this, make sure you stick to your word and do not give him something unless he does his part and you have proof solid that he actually got the GED.
Doesn't sound like nudging is working. I would set clear boundaries and limits up and let him know a DATE that you want him to move out.
If you make it January 1st or his next birthday, you can almost make it something POSITIVE. Something to look forward to. A celebration of sorts. Try to avoid making it a punishment or a negative. He might want to embrace the opportunity to move forward in life if he is able to do so.
As best as you can, try to get your emotions out of all of this. Be like a non involved police officer. These are the facts, this is what I need you to do, these are the consequences if you don't do it....let's move on....
Items that you might find helpful:
There is a book called Boundaries by Cloud and Townsend(authors).
http://www.amazon.com/Boundaries-Wh...5902/ref=sr_1_1?ie=UTF8&qid=1317681179&sr=8-1 This is one of my favorite books.
Two other VERY good books mentioned here are:
Setting Boundaries With Your Adult Children:
http://www.amazon.com/Setting-Bounda...7301352&sr=1-1
(has some religious information...might not be for everyone)
When Our Grown Kids Disappoint Us: Letting Go of Their Problems, Loving Them Anyway, and Getting on with Our Lives :
http://www.amazon.com/When-Our-Grown.../ref=pd_sim_b1