I haven't had this scenario, not looked into it much, That said...

If the module won't be loaded, there won't be AS MUCH of a performance hit, but there will be some, obviously, for having to check an additional 200 modules. Not sure what that is. Though for an admin - That page will be terrible.

If you are requiring 200 separate modules on a single page - I'd have to say you have a design flaw.
For maintainability and flexibility, I think it'd be worth it to check if there is a module [free or commercial or do custom] that can perform the same operation as 200 modules in a single module.

For example - Documents. If each role had access to different modules it would be a good idea to something like DMX Document Exchange module [http://www.snowcovered.com/Snowcovere...] to reduce it to a single module.

It will probably work fine for the users the way you describe, but I'd never want to touch that page as an admin, ever. Or if I had a bunch of the roles.

I don't know what the content is, but I would reconsider the method for getting it to the users to reduce the 200 modules to as few as possible.