If the AC button is off, the AC should disabled as far as the auto mode is concerned. The auto mode will still vary the fan speed, duct flaps, and heater core based on the desired set temperature and the measured temps, sun intensity, etc. So you could drive in cooler seasons this way and never realize you had the AC mode disabled unless you needed dehumidification and it wasn't happening. In warm weather, it will blow more air like the vent mode of a car without AC.
With the AC mode on, it will do all of the above but also keep the temperature and humidity under control even if it is hot or wet outside. A normal year-round setting for an Audi would be to just leave it in auto mode with AC on and let it do its thing. But, I'll turn my AC off for a few reasons... saving fuel, having noticeably better acceleration, and letting the AC condenser dry out so my car doesn't develop a funky smell from always being wet.
The one thing I've always disliked about the Audi auto climate mode is that it doesn't understand the different seasonal comfort goals I might have when first starting the drive versus on long cruises. Generally, I find that I want a lower set temperature at the beginning of the drive but then slowly increase the temp after 30 minutes, 1 hour, etc. I'm only talking about my own body, not effects of the car itself being hot or cold from its parking conditions.
In summer, this is because I am hot from being active outside the car but then cool down as I sit still until eventually the air feels too cold. In winter, the same applies about activity before entering, and I'm also adapted to the cold air on my skin when I first get in, but after sitting still I can start to enjoy some warmth... As a result, I might start with a setting of 68F in summer but end up closer to 73F on long drives. In winter, I might start at 65F or "LO" and then end up around 68F on long drives.