You do. At a Bellagio stay last month with very long lines at check-in, we used the MGM Rewards app to check-in and get a mobile key. At check-out, FHR dining and breakfast charges were credited appropriately per FHR terms in the folio. There was also a small FHR wi-fi credit applied against the daily resort fee. I don't know if checking-in in person would have produced a room upgrade, but the front desk can definitely see you're booked on an FHR rate when producing the final statement.