Will my car fail inspection because the check engine light DOESNT come on?

Yup. That's part of the self-test the system performs when you turn on the ignition switch. Yes, some cars are very expensive to work on and you have one of them. Where you're getting derailed though is in assuming it's a burned out bulb. That bulb turns on so seldom that they rarely burn out. Usually the Engine Computer isn't turning the bulb on.

Regardless if the bulb is burned out, there's a wiring problem on the instrument cluster, (which is a computer module itself), a wiring problem in the car, or an Engine Computer problem, if the bulb can not be turned on, you will never know when a fault has been detected. You won't know that emissions have increased; that's why it won't pass the emissions tests. It's not that the car is polluting more than allowed. It's that you won't KNOW when it starts polluting more than allowed.

Removing the cluster is quick & easy. Lower steering wheel, remove upper
steering wheel trim piece, remove 2 screws, pull out instrument cluster.

Steering wheel can remain in place.

Could be a bulb issue, wiring, cluster or ECM. If you are not the
original owner. Maybe someone tampered with the system to keep the
light off.

Thomas