If the shadow isn't bitmaped with the image, you may be able to edit it using either Illustrator or a PDF editor. If it is, you have some Photoshopping (or GiMPing if thats your preference) to do on the bitmap itself.
The short answer is yes, you can.
The longer answer depends on the tools you have at your disposal. My path: Try to open it in Illustrator, if it opens with no errors, see how the drop shadow is accomplished (bitmap or vector). If it doesn't open properly, try converting the fonts to curves using a pdf editor (Pitstop is my fav). If the shadow is vector, hooray!, change it and save as (never over the original pdf).
If it is in bitmap, try and isolate the bitmap and open it in Photoshop, then (because the bitmap will most likely not be in layers) mask the shadow from the main image and adjust the darkness or levels to suit.
