Assuming your thermostat is working properly, yes, it will disengage. But again, if it's working properly, it will disengage at different temperatures depending on the setting. If you set it at the coldest, then it will turn off the compressor at a lower temperature than if say, it's at the halfway point. IOW, mas malamig yung ime-maintain nyang temp.
So I don't buy it. I set my thermostat to the coldest possible setting that's comfortable for me and my passengers w/o freezing to death.

Fan speed? Again, it depends.
HTH.