Brief Answer:
Hi and welcome to HCM
Detailed Answer:
It is possible but not likely. during reposition of nursmaid elbow, doctor manipulate with radius and humerus is usually held in fixed position. So I dont thing that some more damage was done by doctos. However, Some doctors recommend Xrays before reposition is done to rule out such incidents,but other dont do xrays because nurmaids elbow is the first thing to think of and child iradiation should be avoided. So I dont think you should blame doctors for anything. it is important that he recovers with no consequances. Wish you good health. Regards