No. All Notes/Domino backend classes should only be accessed by Lotuscript when you call Java code using LS2J.
In Lotuscript code, all NotesSessions objects point to the same object as well (despite being created multiple times using New NotesSession), so there is no need to pass it to different functions.
However, in Java, you can have multiple JavaSession objects, so you should be passing a single JavaSession object to different Java methods to avoid wasting system resources.