Installing WordPress into a user directory without any admin privileges

Well, you need a database. That seems like the biggest hurdle you’d face without any sort of administrative control over the server. Can you request a MySql database from the school Tech Dept?

If you can get that, and you can run PHP scripts, it seems like you’d have little issue setting up a wordpress install as it runs on top of whatever server platform your school is running. It won’t need access to the server itself. However, you are going to need some means of getting the actual files onto the server.

If you can secure the database, along with a user for the database, I would install it and see what happens. Who knows what kind of funky permissions they have setup on their server.