For Queue Item views we should be able to gets results when searching on a Case Number in the Quick Find search.

The grid search relies on the columns defined in the Quick Find view of the specific entity. In Customizing if you select any Quick Find view, and click the "Add Find column", you cannot select columns coming from related fields. Therefore, even if you have added the Case Number (a related field) as a View column for the Queue Item, the Quick Find search will not work.