What? I know this is a stoner site but really... Yes, if you put your AC on energy saver mode ie. AUTO, it will save you energy ie money. The only way it wouldn't is if your using an incorrectly sized AC for your room/application or your sitting watching it 24/7 so you can turn it off/on at the perfect times yourself. AC units are designed with the Auto button, it 'may' put 'slightly' more wear and tear on the fan motor, but it will not unduly wear-out one, or any of the other AC components...
The only reasons to leave it "On" would be if didn't have a regular fan circulating air in your grow room like your suppose to or you don't mind wasting money...
"Auto" will shut off the fan (about 90% of the time), unless you have one of the new and expensive systems which can vary the fan speed to maintain temp.