Yes after doing that myself and running it for a while now. Battery's have never experienced temps over 24C.
I would make it standard procedure on large (full house size) offgrid systems in Australia. Battery's and power electronics sucking in icy cold air on a 40C day is very comforting feeling knowing you can hammer the system all you want and its going to stay comfortable.
The AC only operated on hot sunny days and you always have plenty of PV energy to spare on this kind of day so it works hand in hand.
The only alternative would be to some how have your battery's deep underground to stay cool. Though you would then have to have your power electronics in a separate room or they would just heat it up. refrigeration gives you way more flexibility . Not to mention zero dust a big plus on a dirt road.
My room isn't cool room material but its solid concrete block walls, Concrete floor, ceiling is double insulated 3" foil blanket under the tin and 2nd layer of bats between that and the fiber sheet ceiling.
Offgrid 2008, Selectronic PS1 6kw/48v inverter, x 2 Midnite solar classic 150 MPPT, 3960w NE PV 24 x 165w BP panels, 4200w NW PV 21 x 200w DAQO PV, 16x400ah lithium.