I did install it an it does work. However, it works on a site-by-site basis from what I can tell. I don’t think it cleans the whole network. And I’m almost positive it won’t remove those old sites from your database. This is a feature I’ve asked several plugin developers to create/add. When you delete a site in Multisite, it leaves a bunch of tables created by the various plugins (especially those network activated) that were running on that site. It’s not too difficult to do an audit and see which sites still exist, then delete all those that don’t. However, that’s only true if you have a few deleted sites. It would be super handy for instances like yours for a plugin to detect which had been deleted and remove the remaining tables from the database.
Hope this plugin or some other one will add that kind of network-level multisite support.