That does indeed go against the setting's grain. You see, Academy City isn't a place where people are sent because they want to train their powers; It's the place that gives them their powers in the first place. The vast majority of Espers (as in 99.999%) are created artificially by going through the city's Power Curriculum Program. No matter how high their potential, they'll never manifest a power until they've gone through the Program. There are extremely rare exceptions to this rule, but from the sound of it they don't fit with the rest of your intended direction. It'd probably be easier to just say that he was sent here in the hope of gaining a power.
His power seems completely fine, as well as being distinct from any other power we have so far. At a guess, he sounds like a Level 2 on the official scale.As far as the other thing, I just wanted to make sure that what he could do was clearly defined, and subject to reasonable limits.
What power level would you say he is at the moment?
Oh, and the word you were looking for is 'psychometry'.