the problem with your theory is that no matter how good your circulation is, if you are bringing humid air into your grow room then your flowering plants will suffer. high humidity is a problem in flower and can lead to a bunch of issues. i agree, if your a/c unit can handle the dehumidification of your room than great. problem is, most ac units if sized correctly will run almost constantly when the lights are on. an ac unit can only dehumidify when it is cooling. so when the lights are off and the unit does not run as much you need a dehumidifier in the room normally. worse than high humidity are humidity spikes. if your room goes from 40% humidity with the lights on to 65% with the lights off then i can guarantee you will have problems.
also, for those who don't run ac units and only cool with fans then everything depends on your ambient humidity. since your plants are giving off moisture most of the time your room will be slightly higher in humidity than the ambient air. either way, if you have high humidity where you live or grow then you will need a dehumidifier. almost all dehumidifier have digital controls. i'm not saying run the thing nonstop and set it to 15% RH. running your flower room at 35-45% will help you avoid a ton of issues and will also speed up the drying process with absolutely no negative side affects.