Back of napkin math suggests that the water in the lake would sustain drinking, hygiene, and daily bathing for all current MI residents for over 10,000 years, so probably fine.
I wasn't thinking so much about the quantity as the anarchic crowds that'd be competing for access to it (and churning up mud, etc...) if it no longer comes through the pipes. I'm not so sure things would be "fine".
They are already taking their water from rivers and lakes, where else would they get it?