I do think it possible that someone with AS could run and win. Probably their campaign team would have to manage certain things and coach them some (i.e., compensate for or arrange things to avoid their sensory issues coming to light, coach them on and practice eye contact, etc.). Nonetheless, it's possible. It's also possible that due to lack of social inhibition and intense concentration associated with AS, a candidate with the condition might be more willing to be definite in their stances on the issues (something American politics is clearly lacking in many cases) and will actually get things done more if elected.
However, I do think that it will be more difficult than it was for, say, Thomas Jefferson or Abraham Lincoln (both of whom were mentioned earlier in the thread) to get elected. The reason is mass media. When only a small circle of people know what you're really like, and people hundreds of miles away or even in the next town might not even know what you look like, let alone how you act, then it's easier to get the Presidency (more or less...) based on merit. However, when you get the ability to get a candidate on tape and show what they're "really" like to people all over the country, all over the world for that matter, those personal details aren't as easy to conceal - especially when people WANT to know everything about a candidate, however trivial, be it what designer clothing they're wearing, what their spouse is like, how tall they are or if they ever did drugs.
Probably in the modern era FDR couldn't get elected - even though he managed to survive media coverage at the time of his election, it was mostly due to the limited technology, and because the voyeuristic paparazzi culture we now have hadn't evolved yet. Depending on how it was managed, getting someone with a cognitive disorder in the White House could be easier or harder than getting someone in a wheelchair to be President - on the one hand, if well-concealed or for the most part overcome, a mental condition isn't as noticeable, on the other hand people generally have more sympathy for the physically disabled than they do for people whose impairment isn't visible. This doesn't make it impossible, however. Just harder than it might have been at other points in history.