No, a conversation may span multiple SFSBs and other components.
There is always an implicit short running conversation that spans a single request. Any components instantiated into conversation scope during the request will be destroyed at the end of the request.
@Begin and @BeginIf "promote" the sort conversation to a long running conversation spanning multiple requests.
injection/outjection both occur every time the component is invoked. If you think about this carefully, you will see why that is the only possible way it could work.