I do not have personal experience with power stations, but I have watched a bunch of content on YouTube. Playing With Sticks has a nice video on considerations for selecting the right size power station for you - https://www.youtube....h?v=rVU8BVqXxi0. The going rate for a power station is $1/watt so 660W for $499 is a great deal. That is the Costco website price so they may be even cheaper in stores. I do know there is some power loss in translation but I suspect this unit will reliably power a 600W appliance, so you will need to consider your needs. It will not run a 700W microwave or coffee maker.
Your other consideration is how do you plan to recharge it? Based on the picture I believe it has a built in MPT which allows you to plug a solar panel directly into the unit without the need for an interface, but I cannot find anywhere on the website where it actually says that so you may wish to read the box in the store. I think some solar panels come with the MPT attached so you will just need to look for things like that.
If your camping style takes you out for long weekends, you can simply recharge the device from an electric outlet when you get home. But without electric hookups during your husband's six week annual wander about, he will need to determine a way to recharge. There is an equation to calculate the runtime of the power station, but I believe it is something along the lines of this until being able to power a 600W appliance continuously for 1 hour. So if you run your 600W toaster for 5 minutes per day, you can get 12 days usage out of the power station. I believe Playing With Sticks has the equation in his video listed above.
As for using it to recharge the Casita battery, I am not sure that is a doable application for it. It may work, but I suspect it will zap every ounce of power out of it to top your battery off. You may be better served using it to recharge your laptop, phone, tablet, and run LED lights thereby reducing drain on your Casita battery.
Finally, one of the nice features about a Costco membership is that they will take returns no questions asked, so like Clover says above, if the thing doesn't last very long you can always return it. Or if you use it and decide that it doesn't power any of the devices/appliances that you intended it for, Costco will take it back.
If it were me, I would grab the horn of adventure and give it a yank by buying this unit and giving it a go. You really have nothing to lose unless your toaster exceeds 600W. Best of luck!