Perhaps this is a philosophical nuance, but I think a case could be made that high MSE reputation would correlate strongly with success in academia. This correlation is likely not directly related to MSE reputation itself, but to something that a high MSE reputation may indicate: love of mathematics.
As an applied mathematics PhD holder myself, I've witnessed first-hand that success in both PhD programs and academic careers in general depends largely on having sufficient motivation and perseverance to put in the time necessary to develop new insights. I would argue that a high MSE reputation indicates a willingness and motivation to seek out challenging problems in a wide variety of mathematical subject matter.
Moreover, the fact that MSE reputation is not directly related to someone's job or academic position suggests that person is interacting with MSE in their personal time, which indicates that their motivation to participate in the mathematical community goes deeper than just looking for a way to pay the bills.
Thus, if mathematical academic success is correlated with having proper motivation to learn mathematics, and high MSE reputation is an indicator of sound motivation to learn mathematics, then, by the transitive property, high MSE reputation should be correlated with academic success.
Some of the above is tongue-in-cheek, but while the relationship between MSE reputation and academic success is not causal, I think there is likely a positive correlation resulting from a natural selection bias for significant contributors to this site.