The largest battery setup offered by Escape - the two 6-volts combination - is rated at 232 amp-hours... if discharged completely over 20 hours. You get less out if you use it at a higher rate (which would be needed), and it is generally recommended that you discharge this type of battery to no more than 50% of capacity, so the end result is that you could use less than 100 amp-hours.
If the air conditioner needs 9 amps at 120 volts, the inverter running the air conditioner would need more than 90 amps at 12 volts, so the battery set would run the air conditioner for about an hour.
There are long-haul truck drivers who run air conditioning for their cabs and sleepers from batteries, but they have a much larger (and heavier) set of batteries, are cooling a smaller space, and get back on the road with high-output alternator for recharging after a minimum length of stop.
An Australian travel trailer manufacturer offers battery power for air conditioning, but they use a very expensive lithium battery bank.