It's an indicator of whether you have a learning disability or not.
In the case of Randy Gregory and Quincy Carter, it isn't an indicator of an ability to make sound decisions. In the case of Blaine Gabbert, it wasn't a measure of being able to avoid staring down pass rushers, and make good decisions under fire. In Dan Marino's case, it wasn't a hindrance in learning an offense that he was able to drive consistently to record performances.
It's a data point, but in the cases of guys with questionable character, it doesn't indicate anything.
I think the jury is still out on what it might mean for Gregory. With Carter, I think he had other issues going on and it simply got in the way of his development. Who can say what he might have become had he been able to stay out of trouble? I don't really believe that Carter would have been a great QB either way but he might have had a good career in the NFL (not great but good). We will never know for sure. I don't think you have to be a genius to play the game well. I do think that you have to have the ability to learn and understand concepts. As I mentioned earlier, certain positions require more in this area. The ability to see things and make decisions quickly is pretty key for a QB. Marino is not a mental giant but he had some very rare skills and his ability to see things on the field and translate that into action was very quick. The minute he saw something, his brain processed it and his release was lightning quick. Together with his accuracy and his arm strength, that made him great. However, his inability to understand how important the run game was to the overall team was a definite shortcoming and that, IMO, goes to the mental make up or shortcomings of his game. Aikman, just as talented IMO, and perhaps even more so, understood this and that separated them IMO. It's why I rank Troy over Marino, even though Marino has far superior numbers. I do think it was a hindrance but it's hard to make that argument because of what he was able to do on the field.
I don't know that there is any correlation to character thou. I agree with you on that. You can be really, really smart and still be a person of poor character. The reverse is also true. In the NFL, you have to be strong and I am a believe in the fact that character helps build strength. JMO.