This is one of the most misunderstood areas. If a transmission loses all its oil it won’t function at all. All gears will be like neutral. The servos won’t operate the clutches or bands, the torque converter won’t couple if its empty. The car won’t drive at all.
I’ve seen people claim they’ve driven their cars after they had their transmission serviced and the tech forgot to refill it. That’s impossible.
When the transmission is a quart or two low it will warn you by intermittently slipping, especially going around corners or up steep hills. Usually just adding fluid will correct this with no damage if you catch it right away.
Edit - Now if it were a manual transmission that would be entirely different. It would suffer severe damage.