Our company has had trouble with IE11, not just in Moodle, but in other areas, even other Microsoft manged platforms. We were advised by Microsoft CRM to roll back our install of IE to 10. 11 is twitchy with a number of things, Moodle definitely among them - particularly with the loading of files via drag and drop and the display of SCORM packages.
If your courses offer any SCORM packages, you'd save yourselves some student headaches by recommending Firefox or Chrome. Not a single course has ever been marked as complete in IE11 when it contained a SCORM package, and in a number of instances IE11 froze up mid-session