Brandon,
If you facet on "fedora_datastreams_ms" which contains all datastreams an object has, you get exactly what you are searching for
Example
"fedora_datastreams_ms": [ "AUDIT", "RELS-EXT", "OBJ", "DC", "MODS", "TECHMD", "TN", "JPG", "JP2", "POLICY" ],
issue is of course, you need at least one object with a PDF datastream to be able to filter-facet for objects that don´t have PDF. But that issue is present in any non custom solution.
Diego