Perfectly possible I should think, as Garrett says look at DUCKS. We've added a 'piety' concept where piety is accumulated by cities.
There's no reason why you can't add a health mechanic where the health of each city is stored in Lua, and displayed alongside other stats in-game as if it's a core value and influences other things such as food or population or happiness via lua calls to the city class. You could also edit the help text for buildings / social policies, and add XML tables to represent techs / buildings / policies effects on health. You would have to borrow an existing fonticon though (the icons that are used inside help text, like the tiny culture icon or great people point icons, until these are moddable.
It'll be difficult to get the AI to pay attention to the health system, mind, with respect to the buildings it builds etc. But you could tweak the flavours of stuff like buildings to encourage the AI to take care of its cities health, it just wouldn't know that's what it's doing it for and wouldn't be able to react to particularly low or high health to capitalise on the system.
That all said, the patch notes for the imminent patch indicate (though this is speculation) it may be soon possible to do things like replace the decision making processes of the AI with lua script, which would mean you could code lua to make the AI understand health properly.
