Will the start and/or end dates for a course change in Moodle if they have changed in Banner?
No, they will not. Once the course itself and the start/end dates are loaded, they will not change in Moodle.
You can manually change the start/end dates for a course in Moodle (when you are in a course at the course home page*) by clicking "Edit settings" in the Settings block, then in the General section edit the "Course start date".
If there is a more global change for a lot of courses needed, contact your MCMoodle administrator.
* To make sure you are at the course like it is when you first click on it, click the course name in the yellow bar at the top of the screen.