If the question is
Does the higher amp draw mean that the compressor runs for less duration when it does cycle on? the answer is mostly yes.
But, the 9 amp inverter load for 5 minutes per hour is not equal to the 3 amp 12vdc for 15 minutes every hour.
One factor is Peukert.
A fully charged healthy battery rated at 100AH can support a 5 amp load for 20 hours before voltage falls to 10.5v, but it cannot support a 20 amp load for 5 hours. The higher the load on the battery the less capacity it has to give.
Also the 5 and 15 minutes examples above are just made up numbers. I have no idea how long your compressor will run each hour, or how it would compare to the same size fridge running on a Danfoss compressor in the same exact conditions.
My danfoss compresor, if I return the resistor to speed up the compressor to 2500 rpm from 2000rpm, amp draw goes up by ~0.6 amps, but the time the compressor runs will be less.
But the lesser amp draw for longer, is more efficient and keeps the load below the 4.5 amp load at which my battery earned its 20 hour capacity rating.
YOu should ge the kill a watt meter, because actual data lies within, and then one can determine how much battery capacity is required, and how much recharging capacity is required to keep the fridge powered anf get a respectable lifespan from the batteries powering it.
Everything else is a guess, edg u muncated or not.
The Kill a watt is ~25$. A great tool for living on battery power is the DC Clamp on Ammeter. These can be had for as little as ~35$. With it, on One of your inverter cables while it is powering the proposed refrigerator over a period of time, One can also get a good idea of how much the fridge will consume, and be able to use the tool later for other things/loads/ charging sources to see how many amps are flowing.
The following product is an example, not a personal recommendation as I do not own this exact product:
https://www.amazon.com/Uni-T-UT210E..._UL160_SR160,160_&refRID=17NS2HT4J7CBCEWYAAKF