I did not look whether such a study exist, but I want to reason why it's futile to conduct such a study.
Rock climbing performance depends way less on finger strength than most people assume (especially the pinky). To quote the teaching material of the german alpine club, a climbers' performance depends not only on physical precondition, but to a large degree on technique, tactics and psyche. Add to that the physical training which is no doubt necessary for top performances. Of course finger strength is crucial to climbing, but laymen often overerstimate its importance. Go to any gym and you will see people hangboarding everytime that they are in the gym, but never doing technique drills or discuss their pacing.
The gist of this answer is, that the strength of the pinky will likely not be relevant to climbing performance at large, even among professional climbers, because before that becomes relevant, a whole lot of other factors are. Therefore it is unlikely that one could conduct a study which can link pinky length to climbing performance
I know that Adam Ondra is somewhat obsessed with his pinky and asked about how he could use his pinky when getting info on some routes, but the very best rock climber today thinking about his pinky a lot, does not make it relevant for performance, especially in the 5.12 range.
Add to that, that climbing is not as professionalized as say football and it is very unlikely that such a study was ever conducted, or that it ever will produce sensible knowledge.