I would keep the VC.
With all open differentials, the maximum torque that can propel the vehicle is equal to the tire that has the LEAST traction of all four. So if one tire is slipping on ice but the other three tires are on dry pavement, all of the engine's power/torque/rpms will be routed to that one slipping tire on ice.
If you have a center VC in that same situation, you will not get stuck.
With all open differentials, the maximum torque that can propel the vehicle is equal to the tire that has the LEAST traction of all four. So if one tire is slipping on ice but the other three tires are on dry pavement, all of the engine's power/torque/rpms will be routed to that one slipping tire on ice.
If you have a center VC in that same situation, you will not get stuck.