As long as there are no bent or broken pins on the processors, which is usually the most common type of damage to the processor, it should be fine.
Check the motherboard CPU Socket and make sure none of the pin holes are damaged and the locking mechanism still locks the processor in after you removed the stuck CPU Cooler.
If the processor has bent pins than you can very carefully unbend them back.
It there are broken pins or you break a pin while unbending them then there is not much you can do except install the processor and see if it works correctly or not.
By the way, Bent or broken pins on a AMD Processor automatically voids the AMD Warranty.