School districts always use a proxy to filter what can come in / go out to the Internet. In my school district, Amazon is not filtered, but other sites such as Youtube, Ebay, Craigslist, Yahoo Mail are filtered.
I don't ever plan on taking my Echo to school, but it should work as long as you use the correct proxy server during setup. Of course, if your school filters Amazon, then there's nothing you can do about it.