Ministering beyond and taking risks

Eli is 20 years old. He attended YD for at least 8 years. He dropped out of school years ago, but he got his GED this past winter. He's homeless and jobless. He just left here in tears because "the system" isn't working for him. His choices have burned bridges with his family, and even some of his friends. The friends he has aren't terribly healthy. Our target audience is 14-18 year olds. Eli isn't even an old high schooler. I want to pursue him, but my job description doesn't fit his age. Do I or don't I? As a youth and family pastor, the answer is easy - YES! On the other hand, with his lifestyle and beliefs about God, would I have ever seen him in a church? Can I, as a youth pastor, create a place that embraces this kind of student, while also caring for the students who are more "church friendly" (according to our church's culture)? I want to, but will the name "church" carry a stigma that I can break down?
How can I live radically and love Eli? What would it look like to "step out of the boat" and love him with risk? That scares me. Yet I want to be Jesus to this young man. Could my stepping out be the straw that broke Satan's hold over him? Even if it's simply another watering can on the seed that's planted, isn't that a good enough reason? God help me!!