Thank you, Tyler for the response. 

I see that my line of questioning was misinterpreted though. 

The character I have in mind is all about improvement of self, and is self-disciplined (martial arts background before the mutant thing erupted on him/her, and has continued with their training.) In the original version, the Sentinel program was in play, and after running from home, he was targeted more than once. And there was also the Mutant Registration Act that was ongoing. While I don't think the Sentinel thing has come up here, the MRA certainly could have. 

Everyone hears rumors. Mutants being rounded up by officials in the middle of the night and sequestered off to camps, and being summarily disposed of, or experimented on. Things like that. (Think Auschwitz). This is similar to what is currently going on in conspiracy theory movements about FEMA camps an the like now. (Just do a little research and you'll see what I'm talking about. Being on the run, and pretty much homeless, he'd be talking to others on the street, and of course internet cafes would give him access to things as well. 

As a result, he/she (still not decided) doesn't have a mailing address. They don't stay in one place for too long. something like that would have to be hand-delivered, or even reverse pick-pocketed into his possession or something. Which is why 'he' (my character) would wonder how the letter even came to him. How he was found. He's they Gray Man. Nobody knows he exists. Or do they? That kind of letter would make him suspicious. What do they want? Who are they? When and where was he spotted? How did they get the letter to him? Is this real? - He would investigate. Thoroughly. He didn't exactly have a normal upbringing. He would first pull up all information he could on the internet. Every image he could grab, every detail he could glean from social media, encyclopedias, the schools website, any web traffic he could account for to the school. - Upon gaining contact information, and location, he would probably make his way there and recon the place in a concealed, camouflaged position from outside the perimeter. Paranoid? Yes. Rightly so. With his line of experience before the school, it would be within his skillset and method of operating. He might then set up a face-to-face meeting with Admissions, and possibly the Headmaster or Dean. (This would have also included a letter of inquiry before filling out the application). 

This is all based on the concept that academies and finishing schools, places of higher education do not solicit applications from homeless, runaway people that may or may not be on government watch lists (the original version, this guy got into a fight with three people stealing his motorcycle and threw a blast of energy. It missed and destroyed a few hundred thousand dollars worth of cars in a car lot across the street. Completely an accident, but... people like to overreact, and there was a lot of property damages). So, unless they could clear his legal matters up.. over something accidental, and at the time out of his control... And they might be that powerful, but because of his history and legal status, he would definitely question it... and take steps. 

While I personally know it's legit, or mostly seems that way, and I know what things are about... He would not. He/she would question things, very hard. - If it turned out to be genuine (and it would be) then his application might be much more shining and polished. Which might well demonstrate the kind of person he really is, but this is not likely to occur at the drop of a hat. Do I think he would go to the full length of doing recon and all that quickly? No. If he felt as though there were deception or that his gut told him something was wrong... certainly he would. Most likely, he would choose some middle ground. Calling Admissions and Administration. Probably visiting the campus, getting to meet some of the staff, and getting to see the place. Which would probably change his tune. 

Would it be possible for him to have called and visited before hand?

The main idea I've had is that this character's powers aren't fully in control until sometime later. He's spent most of his time suppressing as much as he could. They have a vast potential though, and with his level of creativity and intelligence, he can do a great many things, virtually limitless within certain bounds of electro-magnetism as we understand it. 

Would this character be disruptive to classmates? No. Most might not even know he's there, except for the ones that are in actual classes with him, and he makes his presence known. Destructive is subjective. A lightning strike could be destructive and disruptive. Whether it's to the tree in the back yard, or to the house's powergrid... or some marauding super-powered badguy.. makes all the difference. And one might be target practice, one might be sneaking back into the dorm, or an outburst of emotion... and the other would be something more intentional. All are destructive though. Jus' sayin'. - As for what you actually mean... No, outside of deliberately using powers in a structured setting (a class), no. Small outbursts (such as smelling like ozone when irritated, or having a tendril of electricity lick at their clothing or skin, or over their hair when having a flash of anger or excitement... which might fry something electronic if they're holding it... but that's not intentional)

This character would probably be looking for a way to be more 'normal' - better control, both at keeping their powers from flaring up, as well as being able to let them off the chain and pull out all the stops... to reach their full potential. They'd be looking for a place to fit in, somewhere they feel they belong. And where they can express the way they think, the insights they have, without being told 'you think too much' and the like. Their skillsets and upbringing take them outside the normal scope as well, so that puts them as an outsider too, but maybe they wouldn't be as much of an outsider there. So a sense of normalcy, acceptance... But this character I doubt would ever be 'ordinary'. Maybe he needs to be okay with not being ordinary, but being extraordinary? 

So, I'm not saying that this character wouldn't fit, wouldn't work, wouldn't want to be there. Just some of the world view, and how things might look at first glance... and I'm kind of using here as a sounding board, thinking out loud. 

Probably seems like a lot of babbling. I dunno. I should shut up now.