In Minnesota, none of the standard insurers will write stand alone health coverage on a 17 year old. However, the Minnesota Comprehensive Health Association - which has long been in existence specifically to provide real health insurance coverage for those who cannot obtain it in the standard market - would accept the 17 year old.
A few states do offer "child only" health insurance plans but most don't. Prior to Obamacare any child under 19 could have their own policy.