A:Answer Depends on what kind of battery.
If you're talking about household batteries, no.
If you're talking about a heavy duty battery such as an ecoflow delta 1300 power station, then it could, technically, but only for a while (maybe an hour-ish). Not long enough to justify the expense of the ecoflow - the 1800W one costs around $1000 on average. They do have a 3600W which costs around $3000 which would run it a little longer. You could add additional batteries and delta pro solar panels to run it for a day, but that gets exponentially more costly (starting at around $4000). So you're looking at almost a $10,000 expense to be able to run this all day off battery power.
Gas generators are far less expensive, and could run this. But since gas generators need to be outside you would likely need to get a heavy duty extension cord. Using the wrong extension cord comes with it's own risks (fire hazard), so be sure to get professional advice before attempting something like that. The user manual clearly states not to plug this into an extension cord (same for the other air conditioners I've had), because it is not safe if you use the wrong kind. High risk of fire, injury, or death. The safest thing to do is to plug this directly into a wall outlet and use it as intended.