Unfortunately, the Disney pastry teams do not. But you could order ice cream at the restaurant or from room service to go with your cake!
Amorette's does not deliver to the Disney resorts. You'd need to go pick up the cake.
I see this a lot with wedding cakes, so I don't know why you couldn't have it done with a birthday cake...
\
That cake is covered in smoothed-out buttercream. The logo was printed on white chocolate and adhered to the buttercream.