Only way to find out is by installing the processor on the motherboard and see if it boots up or not.
If it boots up then I suggest your download and run OCCT CPU, GPU, & PSU Stress test and see if it crashes during any of the 3 tests.
by the way, your AMD 3 year Warranty is voided due to the broken CPU pin.
EDIT: If that is the correct name for the broken pin then it looks like a data pin for the processor. So most likely it might not work correctly with that data pin broken.
You can look at Youtube video that shows how you can bypass a broken pin on a CPU by installing a pin on the Motherboard socket corresponding to the broken CPU Pin. Thus when the CPU is installed the pin inside the Motherboard's socket makes contact with the broken CPU pin. But you might end up ruining your motherboard if it doesn't work if you can't remove the install pin on the Motherboard's socket.
Also depends on the type of Motherboard socket you have.