Mapping Center Answer:

Yes, but not much more complicated than what is shown in the Oregon Earthquakes example.  Instead of one polygon with one level of transparency, the map you show can be done by using the Buffer tool to create progressively larger, though only slightly larger buffers that are set to be transparent--you should need 7 to 12 buffers to make the effect look good (the larger the shadow, the more buffers you will need). 

Optionally, you may also want to use the Erase tool with the original polygon being erased from your area of effect polygon.