No, the OBD system is part of the ECU internal engine control system and is not controlled by the MIL lamp. On the contrary, the MIL lamp is controlled by the OBD system according to the corresponding strategy. It is also part of the OBD system. Turning off the circuit of the MIL lamp will make the MIL lamp unable to alarm, but all the fault diagnosis functions will still run. For the system with the MIL lamp circuit connected to the ECU, this will not mask the fault, but the OBD system may also detect the fault of the MIL lamp circuit (if the MIL lamp circuit is directly connected to the ECU).
However, the OBD system can automatically suspend work temporarily in the following situations:
Plateau: above 2500 meters above sea level.
Lower ambient temperature: when the engine starts, the ambient temperature is lower than -7°C.
Rated tank volume oil level 20%
The road condition is very bad.