G'day Janelle,

Although we haven't tried this ourselves, the Anderson plugs would match up and both adaptors should plug into the Anderson port. I would double-check with Kings and the Fridge manual to check the requirements to power this fridge to make sure this will run ok. Using another cord may damage the fridge and void the warranty if not correct.

This cable is designed to run EvaKool fridges from a 240v power source, but on paper, it does appear to be able to put out enough current to also charge a battery.
There's no obvious reason why it wouldn't work with a charge regulator but no-one seems to know for sure if it would burn out on a low/empty battery - unfortunately it's not something that can be known until it's tried out, and given that it's not the intended use, it wouldn't be covered by warranty if it failed.

Given that the average 240v battery charger costs upward of $300, I'd lean toward this one not being up to the job.
I'm sorry we can't be of more help!