By auto cook I mean setting oven to come on and cook while I'm away from home. Time to heat up, time to cook, time for oven to cool and chicken to rest.
I think that's a question for your oven's User Manual....
That's impossible to determine without understanding your oven. I'd just experiment a bit with some cheap chickens from the supermarket.
Your scenario seems a bit odd and I wonder if even the manual would totally address. I think most suggested schedules would assume the chicken is removed from the oven at the time it was completely cooked. The come home to a hot dinner thing which is usually what people want. You seem to be planning on eating a cold/lukewarm chicken that after it completed cooking, stayed in the residual heat ( drying out) as the oven cooled. Would timing things so it completes cooking at the time you expect to arrive home work? Even if you do not have to tend to the chicken (other than remove from oven to rest) you probably are not going to walk in the door and sit down to eat 2 minutes later.
In addition to what everyone else said, there would be food safety issues involved with leaving a chicken out all day; if it were not cooked all the way through for example and left in the oven to cool down. And if it's left in the oven all morning and afternoon until the oven is set to heat up. This just seems like a good bacterial breeding ground.