JSF uses a Front Controller. There is a FacesServlet that controlls every request sent to it. The difference between what you are currently using and what JSF provides is a component framework. There are many discussions in this forum on that very topic if you just do a search.
As far as replacing what you currently have, JSF is not mature. It is very new. But it is very stable and works very well. There are some bugs and features missing from the current implementation but you can say that about any framework no matter how long it's been around. With that being said, unless you see a significant reason to replace what you have, especially if what you have is currently working and serving its purpose, then I'd think long and hard about the conversion process and what, if anything, you would gain from reworking the application. If it ain't broke...