question, if this roster is trash, how can JC, let alone any coach win with this roster.
Depends upon what you mean by "wins." I cannot imagine any coach taking this roster and doings with it something meaningful. No coach could make this team competitive for a deep playoff run. In fact, i doubt any coach could make this a playoff team. That said...
JC has been mighty non-impressive. He still plays players who should not see the ice. He under uses players who should be used. The systems and/or personnel for the PP and PK have not been successfully modified to be improved (in fact, both units under JC are actually diminished relative to the same units under Q --- it was bad under Q and now worse under JC). The team under JC has not gotten better. By now, some evidence of the arrow pointing in the right direction under JC should be there - at least a glimmer of getting better. However, if anything, the arrow is pointing in the wrong direction - this team is getting worse.
Sure, this is a bad roster. But should the Hawks be the worst team in hockey? Almost certainly not. Should the Hawks be getting better, rather than worse? Yes. So... thus far, JC has shown nothing to suggest that he can be a long-term answer. It is early, and maybe things will change. His roster sucks, yes... but it is not as bad as what we are seeing. The context for his taking over was not ideal, sure --- but what JC has accomplished so far is... bad.
No, no coach can "win" with this roster --- but at the same time, it is pretty unimpressive that under this coach the team is getting worse.