To the same level that a properly built 727 will- provided you don't hot rod it with OD engaged. Transmissions are really rated on torque output not horsepower anyways.
The last year the Dodge Cummins package used the 48RE OD trans was 2007. Like I stated earlier the geartrain in the OD unit was pretty much the same between gas and diesel.
For 2007 the Cummins made over 600 lbs. ft. of torque. Max GCWR was approx. 20K.
I don't think your torque and vehicle weight will stress the OD like the Cummins will.
