No, you can't.
Reason: The module will have a dedicated flash area for storing the PID. If there is already data in that area, it will not retrieve the PID from the firmware. If the area is empty, it will fetch the PID from the firmware and write it to the flash.
Solution: Taking Telink as an example. Directly modifying the JSON file is useless. You need to use the original manufacturer's tool to completely erase the firmware, and thenclick on the setting and select 1016 to erase all the authorized burning.
Finally, re-burn the new firmware and authorize it with the Tuya module, and you're good to go.