like newt said, yes C3 works well on all those platforms, and C3 is great to quickly prototype something.
but for any kind of app that will be used by many users, you will need a backend system that has the capacity to handle the traffic - that would have to be developed in something else.
and there are security issues. privacy issues. etc.
C3 does not have native push notification support - which will probably be a problem for you. And C3 doesn't use native UI elements the way your users might expect - you have to replicate that yourself, which can be quite difficult. It all depends on what you have in mind.