Asking a Professor for a review of a university application research supplement
It is definitely not inappropriate. But professors are busy people, and you are likely to be put in the "crank" bin without a detailed reading. Be careful crafting your email, and ask some of the staff at your school to review it to minimise it.

If after a reasonable time you don't get a response, you could try to find a student's association at the university related to your research. They could probably be able to judge it, and take it to the professor in person with their "seal of approval", that is more likely to get his attention.