I am installing 18" wheels on my ATS,with the same size tires that cadillac offers on other ATS models
Mine came with 17" wheels and and slightly smaller tires, my question , will I need the dealer the
Adjust the computer ?

no you'll be fine

The larger wheels/tires come with a smaller profile tire, so your tire diameter remains the same: mo need to reset the computer for the 18" wheels.