30amp at 240v of power is completely enough to power most any home's air conditioner, since most a/c units of the larger size use a 30amp 240v breaker - the output to the air conditioner is at it's highest for a 1/4 second when the compressor 'kicks on' at the start, and the a/c then uses closer to 20amps or even less while actually 'running', whether for 10 minutes or 10 hours.
The ProPower from the truck's battery pack can either be accessed from the 240v 30amp outlet from the bed, ready to go, or you can certainly choose to pay the additional $5,000 to $10,000 for the additional ProCharger and Inverter and related home equipment to allow the truck to just 'plug in' to your home, during an outage, or, as you suggest, to possibly 'run' your home during the hot daylight expensive hours, while then 'charging' from the grid during the overnight 'lower' rate timing.
I think this idea, though, is not going to be efficient for the long term. While the battery is able to do this, having this output and input constantly day in and day out, while also using the truck to 'drive' somewhere at other times, may not be practical, and you may find that the battery wears out well before you might expect it to.
One of the issues is that you are trying to defeat the incoming grid power, when your truck is parked and available for output, but you then need that grid power when you need to drive the truck. That sounds like a lot of 'manual' transferring of power on a constantly needed basis. If looking to automate that you'll be spending a LOT more money than just using the grid power to power the home on a daily basis like the rest of us.
It's an idea, but probably not a good, or practical, or even financial one, in the long run.