I know most people are going to think your plan is crazy stupid, but personally, I think it sounds like it could be an interesting experience.
If you go through with it, you should keep a journal. You'll come through with an understanding of functional homelessness that even a thru-hiker doesn't have.
You'll likely make yourself a social outcast. Most women aren't too interested in homeless guys. It sounds like you're plenty young and can do stuff like this without long term consequence.