Nope.
Open differential differentiates torque evenly between the two wheels, not motion. The tire with the least available resistive force (friction) will determine the torque applied to both wheels. Remember torque is a result of force. If you have one tire on a sheet of ice (no friction) and one tire on dry pavement (friction between tire and pavement) then the tire on ice will spin while the tire with traction will remain stationary. If there is no friction between the tire and surface it is on, then hypothetically no torque is required to rotate that tire. Essentially, both wheels are receiving zero torque as a result of the available resistance at the tire with the least traction.
Same thing will happen with an open differential during articulation if one tire comes out of contact with the ground. The tire in the air will spin, while the tire on the ground will remain stationary.