Did you add an extra zero there? An 1100 amp hour battery would weigh approximately 575 pounds, and would power a fridge for a lot longer than 2.5 days.
If you meant 1100 cold cranking amps, that has little to do with storage capacity rated in amp/hours.
Another thing to note is most True deep cycle batteries do not list a CCA rating, as they are not designed for starting. Which is what a CCA rating is designed to infer. Nor will a starting battery hold up well to deep cyclic use.
An alternator with a rating over 60 amps is useful, only if there is a single or multiple AGM batteries with thick cabling to absorb the extra amps, or the vehicle's electrical demands are regularly above the 60 amp threshold.
An alternator rated for higher amps will not produce any more amperage at idle speeds, unless the alternator's case is physically larger, or the drive pulley is smaller.
Most vehicle's stock charging systems lean toward safety. They are not concerned with slightly undercharging a single starting battery. They are concerned with overcharging one. A chronically overcharged battery will off gas more, and make it more succeptable to explosion. So they design the voltage regulators to limit the voltage earlier than the battery would really like, and they save money by undersizing the cable.
This makes it even more difficult for the alternator to fully charge an additional battery.
If you are going to rely solely on the alternator for charging, one should upgrade the wiring, and keep the distances between battery and alternator as short as possible. Keep in mind a warm engine and alternator produce very little current at idle speeds, and it can take anywhere from 3 to 8 hours of driving time to bring a single starting battery from needing a jumpstart to being 90% charged.
