Can I filter the backlog items shown in the "Backlog items that are not assigned to any board" box?

Yes, if you create saved filters in the Backlog tab, these filters will also be available for use in the "Backlog items that are not assigned to any board" box in the Kanban tab:

Tip: Make sure you save the filter, by clicking "Save this filter" inside the filter box in the Backlog tab. Otherwise, it won't appear in the "Show" dropdown.