Which model of 小米max? For Max1, there are two versions of ROM (MI MAX 32GB and MI MAX Prime) and you don't need to unlock bootloader to change ROM from CN to Global ROM if you choose local update.
The ROM you post V10.2.2.0.NBCMIXM is for MI Max1 32GB version. Since your phone has 128GB ROM, your should pick Max Prime ROM (V10.2.2.0.NBDMIXM) if your phone is Max1