Yes. The only difference in our BB cups between 24mm (Shimano) and 22/24mm (SRAM GXP) is the non-drive side bearing and outer dust seal. Both bottom brackets use the same 24x37x7 bearing on the drive side with a matching 24mm ID seal. For 24mm (Shimano) cranks, the non-drive side cup uses the same bearing and seal. For 22/24mm (SRAM GXP) cranks, the non-drive side cup uses a 22x37x8 GXP bearing and a matching 22mm ID dust seal.
If changing your bottom bracket to a GXP compatible unit, you will also need to add a 24mm ID wave washer to the drive side between the dust seal and the crank arm.