think it's a serpentine belt. did this for 9 months on a kia sedona "04. then when money saved, replaced it. it ran fine during that time. can belt be bypassed while avoiding a/c compressor on the '09 sonata? (tried that with sedona but belt kept breaking anyway. so removed compressor.)
Unplug comp. elect. connector does comressor belt PULLEY turn? Not the center but the part the belt runs on.
Clutch hub can be removed if need be, then if pulley is free the compressor becomes just an idler!
if the clutch and/or pulley on your compressor are okay, yes, you can continue to operate your vehicle without any issues...without a compressor you will need a bypass pulley and special length of belt.