I have an electric gourmet Brinkman, haven't converted it or anything but I would figure you could just add a grate to the bottom and burn with charcoal as opposed to the electric element.
Only thing you need to think of it airflow/heat adjustment mods.
I use my Brinkmann Gourmet either way. I use a modified grill wok for my charcoal basket. Seems to work quite well, and the results have been better than I expected. I control the air intake with a magnet partially blocking the hole where the element cord passes thru the 2 pans. You can do the same thing with the Char-Broil.