Note: This definitely DOES have -3 MP drain for carby. With the Carbuncle mitts, Carby is free, perpetually while out.
HOWEVER, there IS a catch... The SMN Auto-refresh ability appears to be either a) disabled, or b)(more likely) Carby cannot be reduced lower than than a 1MP cost (thus effectively negating the refresh ability).
So SMN beware - Carbuncle will not exactly be "free" with this staff - you will not be auto-refreshing while he's out.
Sad, but true ><.