Yes, it checks the overdrive records for any books Overdrive has to offer. Individual libraries all refer to the same main catalog for their books, for buying them and offering them to us. For instance, the OverDrive ID this plugin reads from
search.overdrive.com is the same one that identifies each book across all libraries, which is why this plugin works.
If you search for a book there it will also tell you under the individual book results which library systems own it.