We experienced some yes and some no.
At AK, Minnie & Mickey were so slow at their "Camp" they came over to us on a bench and helped us feed our 5 month old. Minnie held DS, while Mickey held the bottle. DW provided back-up.
In Toontown, Tigger curled up with DS on the floor. Mickey sat down and held him. Pooh didn't motion to take him so I held DS.
At DS, Sorcerer Mickey didn't motion to hold DS either.
The characters accompanying CM's will tell you "no" they won't hold infants if you ask, but you see who rules the roost when Mickey motions to hold your son. The CM just shakes his head.