I've gather limited information about this question elsewhere. The information might be helpful to other in the future.
"The Moodle Network features does allow in effect a single sign on for multiple servers. If a user logged in on the first server has a course that they are teaching in the second site they will have the teacher role for that course. An Authenticated User and/or a student will inherit those roles on the new server for the courses that they are enrolled in. Server level roles would need to be assigned on each server."