This surgery is usually done as an outpatient, arthroscopic procedure. If, during the surgery, they find that the rotator cuff needs to be repaired (which they usually know before the surgery with an MRI) then it may be converted to a mini-open procedure depending on your surgeon - either way through, you should still go home the same day.
Immobilization for an SAD is usually minimal - a sling for comfort for a few days or a week, and starting therapy 2-3 days after surgery.