i am having ???? regarding how the stock alarm+aftermarket immobilizer work together with turbo timer?

let say now i have stock alarm and immobilzaer in my car, as normal i arm & disarm when leaving & entering car.

but when i install a turbo timer for my turbo car, when i leave the car and arm the alarm while the engine still running during the timer count down, will the immobilzer cut off the enginer?