Actually, it’s probably the other way around. I don’t know that there’s any real evidence of it, but it is at least a common trope that personalities tend to adapt to their hosts, so to speak. So someone with the ability to become invisible will tend to have a personality that supports that. Similarly, powers that are, of necessity, attention-drawing (say, ones that make fire) will create attention-seeking personalities, or invulnerability will create stubborn, stand your ground personalities.

Of course, being a trope, it gets violated a lot, too. And there are obvious cases where characters get the powers they get because their personalities are just so (say, Captain America in his recent origin movie, or the Green Lantern being chosen for bravery, etc.). But on the whole, it seems psychologically reasonable to think that a major defining characteristic of a person will be or become reflected in their personality.