I'm not specifically sure about Cohorts. I haven't tried that before. It should preserve all user data, including cohorts, etc., but I would set up a test cohort and try it first if I were you. I'm 99% sure it will work though.
The easiest way to manage this is probably disabling enrollment method "cohort sync" in "enrollment methods" in a course. This should quickly and easily take those users out of the active participation parts of the course, assuming you were using cohort sync.