Yes, most Disney restaurants can have a special order cake for your meal. I would suggest that you call the specific restaurant and ask how they handle these orders, some will take your cake order and handle it some will ask you to call the bakery directly and order it. Whatever you do, make sure your have your seating reservation number attached to the cake order and call the restaurant more than two days in advance to make sure that they have it noted on the reservation.
Finally, check one last time when you check in at the podium, yes it sounds tedious, but Disney is a very large organization (as you well know) and sometimes different departments overlook sharing this information, a little extra effort on your part will insure a pleasant evening without any surprises.