Yes. In
JSF, you don't "grab" data. The essence of Inversion of Control is that you don't go out and get stuff. Instead the stuff is pushed in to you.
When you submit a JSF request, the values of the controls on the submitted form get sent to the server. JSF validates them, and if they are all valid, JSF automatically updates the backing bean(s). You don't have to "get" the radio button value, because JSF itself will set it for you in your Model (backing bean).
After the Model is updated, the action method or AJAX listener is called (and ONLY if the model was updated - meaning that the submitted data was 100% validated).
If you want the action to navigate to a new page (View), then you'd use a normal commandButton/commandLink and a normal action method. If you want to retain the current View, then you'd use AJAX instead. Unless you wanted the entire current page re-rendered.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.