The ability to have a computer and internet connection are so prevalent today that yes, you can be kicked out and still have access to the internet. I would also think that coming here as one of the first things after being kicked out is not totally unheard of. I would have probably done the same had I been kicked out when I was younger, since this would have been the only place I would have had friends to talk to and for support. Remember that this site is a support site, and to reject someone's story and possibly beat them down even lower seems a bit harsh, especially before you know all the details.
Anyways, Jack, I'm very sorry to hear about your situation. I take it you're in college, right? If so then I would think that they would be open 24 hours like mine was most of the time, and if not then you may be able to talk to them to get help finding a shelter or another place to live. Take care and be strong. Focus on your education and don't let it slip. That will be the safety net you need to get yourself on your own two feet and not have to rely on your parents anymore.