I am retired from my auto repair business after 42 years. I am going to help my son re-gear both differentials on his 2002 GMC 4-wheel drive automatic 2500 pickup. We will not have the time to re-gear both front and rear at the same time. Will it hurt to re-gear the rear and drive with the front driveshaft removed on this vehicle?

Nope. The front axle won't be driven so there will be no bind-up.