Should there be drainage from the umbilical region after gallbladder removal?

No: Unless you have infection or fluid buildup in your stomach called as cites.

Maybe: Small incsional discharge of clear or yellowish fluid can be seen. If there is increasing redness, pain or swelling at the incision then infection needs to be considered ; call your surgeon now. If ino sign of infection ; it does not resolve in a few days, call your surgeon too.