Sort of but not copy paste. Export the image with the drop shadow to EPS from a file the same size as the image and drop shadowed and then Place (control or apple "D") that EPS into the file you are making the epub in.
However your requirement is more simple than that. Just crop that jpeg you posted and place it into the text like the example I just posted.
If you want the text to float around the image you could try looking
here.