I don't think you need to add a pump for the tranny as long as the t-case is in neutral.
The driveshafts turn at different speeds all the time except for when you are travelling a perfectly straight line on a perfectly flat road and all the tires are exactly the same size.
The driveshafts turn at different speeds all the time except for when you are travelling a perfectly straight line on a perfectly flat road and all the tires are exactly the same size.