In short, YES, it will hurt your car if it breaks and you continue to drive it. Turn the A/C off. If it is causing the belt to slip or burn it will eventually break the belt. When this happens you will not be able to drive the vehicle. The belt runs everything not just the A/C. Power steering, alternator, water pump, etc... The A/C turned off the belt should free wheel on the pulley and not cause a problem unless the pulley isn't turning because of other damage. Suggest you have it checked or repaired to avoid being broke down on the road.
Answers & Comments
In short, YES, it will hurt your car if it breaks and you continue to drive it.
Turn the A/C off. If it is causing the belt to slip or burn it will eventually break the belt. When this happens you will not be able to drive the vehicle. The belt runs everything not just the A/C. Power steering, alternator, water pump, etc... The A/C turned off the belt should free wheel on the pulley and not cause a problem unless the pulley isn't turning because of other damage.
Suggest you have it checked or repaired to avoid being broke down on the road.