If he's being sent home, he's probably in medical hold for psychological stuff. It's basically a dormitory for people who lied about not having asthma, tried to commit suicide, or have some other long-term health problems that can't be solved in a few weeks.
Will will probably get out on a medical discharge, which is neither honorable nor is it dishonorable or other-than-honorable. It's just a discharge stating that for some medical condition or some other mitigating factor, he could not complete recruit training and will be further barred from coming back. It shouldn't have very much effect if any on his life or work life, aside from not being able to do what he wanted to do in the Navy.
They'll probably not scream and yell at him because they look at him as an unstable person and they don't want to make it worse or cause undue harm. They'll still be strict and disciplined but as for completely tearing away your humanity like they're supposed to do, they shouldn't be doing that. He just couldn't hack it so they're sending him home.
It's not easy, no matter what service you're in. I was 18, first time away from home, in a place where I knew nobody, getting ready to become an instrument of war and quickly coming to the realization that this is serious fucking business and that all that shit they promised you comes second to you serving your country. Everyone breaks down and cries, everyone has a moment of weakness where they think they can't go on; it's up to the team to help each other out and get past it so you can accomplish what you're there to do. The first two weeks are utter hell, but you have to be of strong mind and character to pick yourself up and forge ahead.
It's not a slight on Will's part at all that he couldn't do it; some people just aren't cut out for the military. That's why basic training exists and that's why not everyone graduates. If I'm not mistaken, Will's probably confused right about now. On one hand, he's relieved that he'll get back to some sort of normalcy, but on the other hand, he's probably thinking that it wasn't so bad and if he could've just held on just a bit longer, he could've finished it and begun doing what he set out to do. There's going to be a LOT of second guessing and "what ifs" in the coming days/weeks/months for Will that will stay with him the rest of his life, but it's nothing to be ashamed about. We all have our limits. What he needs now is support to know that he's not a failure...he just has his limits.