Charger 1 batter source 12v socket?

Instead of connecting charger 1 directly to 12v car battery, can it be connected to a 12v socket? Will that provide the same input into charger 1?
I’m wanting to install in my UTE tray, which already has a 12v socket, so install would be much easier.

Thanks

NO - Your vehicle Ute socket is 12V - 10A max = 120W. At full power the C1 outputs 560W, which at 12.8V around 36A and more on the input side. You will either immediately blow a fuse, or start a fire.
The Charger 1 minimum output voltage is 15V, which will also blow said fuse. Plus, you would get more from the cig socket direct and that is less than 100W anyway.
The circuit breaker on the Charger 1 is 60A, it’s high current, no vehicle outlet has. It has to tap off the start battery, which in turn is run by the alternator when driving. The manual states to start the engine before switching the circuit breaker on, this prevents any possibility of it interfering with starting the engine.

Forgot to mention, the Charger 1 is not intended for under bonnet use. Second point, has your ute got a canopy that is water/dustproof? i.e. out of the weather. It probably won’t like rain or bush dust any more than your power station.
You’re probably better off installing the Charger 1 in the rear seat area as well as whatever power station you use.
I have a Prado, so not an issue for me, lol.