Would removing A/C result in car requiring less coolant?

Removing AC would have no effect on cooling system capacity. Removing the heater core (and heater hoses) would reduce cooling system volume (meaning less coolant needed). The heater core is not part of the AC system. The heater core box does house the AC evaporator coil. If you're contemplating removing the AC system and heater core just be aware that will also remove the defroster. The AC runs to dehumidify the air blowing on the windshield.