can wordpress power something like a school’s website? imagine if a class adobe flash for beginners had three sessions - one on tuesday, one on wednesday and thursday, how would you deal with that?
if it was one session i could see it’s just an article in the system. but multiple ones?
the more i thought of it, i realized that this should be no problem with custom fields. and even better, in the new version with custom post types, it would be even more user friendly to enter this data.
post: class1
customfield1: first block on schedule (in php friendly date format)
customfield2: second block on schedule
post: class2
customfield1: first block on schedule
customfield2: second block on schedule
and so on…
Depends of what you have in mind for your elerning mechanism. If you just want to publish your lessons and the students to comment over it then is ok… And you could to much more if you research over WP plugins. Still… there are sripts for elearning like Moodle like john carter says. Here is a list of other free elearning scripts: http://opensourcescripts.com/dir/PHP/Education/
I don’t see why Wordpress wouldn’t be able to handle the task, the only question I would have would be over the navigation to ensure that relevant older content blogged onto the site didn’t get lost in the archives. In regards to displaying documents, Wordpress will handle the task with ease (in the fact that like all blogging platforms it gives each posting it’s own unique URL which can be referenced and as long as is required), you could quite easily link to the next and previous parts of the article from within the document or if needed attach additional resources such as video, images and other stuff. I say give it a try, you’ve nothing to lose. 
You may want to look at Moodle. It is a Learning Management System like Blackboard but is open source like WP. They have an [URL=“http://moodle.org/about/”]info page and a [URL=“http://demo.moodle.org/”]demonstration site that shows you how it works.