This is a very good question that has not been heavily researched. But according to one study from England, you can run into a few problems along the way. At least half of the patients they surveyed reported loss of elbow motion, some elbow stiffness, and reduced grip strength. These symptoms did affect elbow/arm function.
The good news is that despite these long-term symptoms, the majority of patients involved still rated themselves as satisfied with the results. That may be because even with loss of motion and strength, the elbow wasn’t unstable.
Women seemed to have slightly different results when compared with men. The women tended to be older than the men and more likely to have a fall contributing to the injury (men had high-impact traumatic injuries). But even controlling for these factors, women still reported poorer function after treatment. Surprisingly, the women’s satisfaction wasn’t lowered by the physical limitations.
Not all patients have problems after elbow dislocation. Some come through just fine with no sense that there ever was a problem. We hope that describes your situation in the years to come!