Its not the same on all trannies. Remember to post the year/make/model/transmission/.... when asking a question. There are thousands of members here and some might have 1st hand experience with your vehicle type.
Pulling the cooler line method, on a hot transmission, will remove most of the ATF if enough ATF is used. Most flush machines splice into the cooler lines the same way. I'm one who remembers the older ATF flush machines that hooked up to the ATF screen/pickup in the pan(pan removal required), and the mess that it made when running the vehicle during the flush(with no pan).
ATF through the cooler in most transmission is wasted fluid. Typically, the ATF is picked up at that pan, worked everywhere, and the leftover goes to the cooler(usually exiting the TC). If the cooler gets clogged or restricted(thermostatically or by fluid viscosity) the ATF pressure regulators waste excess PSI back to the pan.
Its good to backflush the cooler once in a while or install a filter prior to the cooler. Newer coolers are less likely to clog. Some of the older ones had thimble screens or small passages that could clog.