Have you found answers to all your questions? I realize this is an old thread but felt I could add to the discussion so here goes...
I went down this road a few years ago and found several aspects of the converter supplied in my Airstream meant the converter was less than optimum. In addition, there are other things that you (and your brother) have not considered.
Several responses to your questions bear repeating and more thorough discussion.
Yes, the 800 watt generator will likely charge the batteries but that's not the entire answer in my mind. Boondocking necessitates more than a simple yes, I can charge the batteries answer.
As mentioned above, the Airstream is likely equipped with a single-stage (aka "dumb") converter. If so, this type of system is not optimum and will not recharge the batteries as quickly as a multi-stage converter. The multi-stage converters have the advantage of charging more quickly and when plugged in for long periods of time will maintain the battery charge in a more efficient manner compared to single-stage converters. If the unit is not multi-stage your brother should consider this upgrade. There are lots of brands on the market - some better than others - I chose a Progressive Dynamics PD9260.
For late model Airstreams like you brother owns, something like the PD4600 shown here is probably the right answer:
4600 Series Upgrade or Replacement Power Converters
Boondocking is not simply about whether the battery(ies) can be recharged. Does your brother have one or two batteries? Some Airstreams only have one battery. Two is obviously better (more capacity) for boondocking. Be sure the batteries are suitable for true deep-cycling. Some batteries are referred to as dual purpose, RV, marine or some other marketing mumbo-jumbo that's not all that useful. Batteries for this application are rated in Amp hours (Ah) not cold cranking amps (CCA). Cold Cranking Amps is for batteries used to start an engine. A typical flooded, lead-acid, deep-cycle battery will be in the range of 80 - 100 Ah. The higher end of the scale is better for more capacity.
Absorbed Glass Mat (AGM) batteries are often touted as superior to flooded, lead-acid batteries. Both are lead-acid so maybe it's more correct to simply refer to the distinction as AGM vs. flooded. Many deep-cycle AGM batteries are on the low end of the scale when it comes to Ah rating. For that reason, I think flooded batteries are better for most RVers but there are caveats to that. Assuming your batteries are in an outside storage compartment (most Airstreams are built this way), flooded is probably the way to go and your brother will likely be able to find batteries that are rated at 100 Ah or even a little more.
I know I'm making a big deal about the Ah rating but it makes a big difference on how often and for how long the batteries will need to be recharged.
Another significant aspect of boondocking is knowing how much power is being used from the batteries. It's surprising to see how much power is drained even if using LED lights. The key is don't use power consuming devices unless necessary. To get a full understanding of how much power is being consumed your brother should consider a battery monitor system. There are a variety of ways to implement a battery monitor ranging from hard-wired to wireless, smart phone monitoring. However, all the systems require a precision shunt to be installed in the system. This is a relatively straightforward modification but it does take some understanding of the battery wiring and a willingness to figure out where/how to install the shunt. It's a do-it-yourself job for some or it can be done by a service technician. Be aware that some service technicians don't understand how to install semi-custom items like a battery monitor system so it's a good idea to find a qualified shop.
Here are two means of battery monitoring - one hard-wired, the other wireless:
TriMetric Battery Monitor
https://teambmpro.com/au/shop/battery-check.html
Hope all is going well for your brother. Even if he has successfully boondocked with his current system it may be worth considering some of the items discussed on this thread.
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