Hi,
Yep, using Fsm for purely game state management is totally inline. I worked on a project where PlayMaker had this role for managing the whole ui windows, modals, menus etc, not being responsible for the actions at all, simply to control views ( states basically).
Fsm can be ran using templates, and you should definitly study sub fsm as well that allows you to run an fsm template within an action ( action: runFsm). that's powerful indeed.
now, there isn't any wrappers to combine multiple fsm. Instead I recommand doing like Ngui ( kind of), where everything is a gameobject, so you would have a hierarchy of gameObjects, each with its own fsm and "responsability", then you work out a way for all of this to communicate without any hardcoded links, typically, using either a fixed/standard hierarchy layout,and the expected interface.
For example, using "get fsm xxx" actions, you can access a gameobject fsm just with defining it's name and variable as strings. so if you object implement fsm "xxx" and has variable "yyy" then you are good. Very powerful, I use it all the time, it's allowing you to create loose connections between prefabs and complex/changing features.
Bye,
Jean