BuddyPress

Is it even possible to add predefined categories for users to choose from?

Single WP install, sure. Just add the categories from backend and users can only choose from the available categories.

If you’re talking about categorizing a multisite blog, you could use something like this http://wordpress.org/extend/plugins/blog-topics/

Or if you’re looking to create categories in main site which are automatically added to new subsites of multisite install http://wordpress.stackexchange.com/questions/12201/wordpress-multisite-global-categories