I guess I'll go against the flow here. If the outside temp is what the A/C would be set at it stays off. I've never been a fan of avoidable noise, whether it be gennys run for hours on end or diesels idling for 10,15,30 minutes in the morning. Noisy A/Cs can be annoying too, especially if it is the only one being used as the outside temp makes it redundant.
Running it to cater to a child? No. Not happening. Never did it to cater to ours. They learned to sleep in different & noisy enviroments from day 1. Lucky them. As adults now they can sleep anywhere.