Don't fly the ATR but the problem seems to be the same as the Dash 8. I don't think it would work, in fact it might even make things worse by reducing the overall airflow. With the air con packs working, the cold air pumped into the cabin is mixed with the hot air already in the cabin (primarily thru the recirc fans acting as mixers) and gradually cools everything. With the recircs off, the mixing process is slowed and I suspect overall cooling rate would be reduced.
Remember that as the cold air is pumped into the compts, the recirc is also recirculating that cooled air.
Hope I said that right.
P.S. We have the same cabin temp problems here - short sectors, average 30C outside, few APUs and fewer ground air con carts. It's amazing the difference with the APUs on after landing and running throughout the turnaround.
One technique used for quick cooling - but the jury's still out- is to set the cabin altitude to 4 or 5000ft and let the cabin climb at about 600/700fpm. As soon as the cabin reaches the altitude, return to automatic operation. The theory is that with the cabin climbing quickly, more air (warm air) is vented and replaced by the cooled air. Some people swear by this.