Can comboboxes have drop shadows, and if so, how (Flash Pro)?

You can do it programmatically the same way you would assign a filter to any DisplayObject...

    import flash.filters.DropShadowFilter

    var cbFilter:DropShadowFilter = new DropShadowFilter ();

    cb.filters = [cbFilter];

Another approach sans AS3 for the same effect would be to just place cb inside a MovieClip and apply the filter to the MovieClip thru the properties panel

Though you will find that it only shadows the main element in both of those approaches, not the drop list portion with the shadow.  To add it to the drop list portion you need to target that....

    cb.dropdown.filters = [cbFilter];