So to answer your question yes and load that is drawn from the system will come from the PV once the battery is charged.
Change the load, less W from the PV, again assuming your battery is full which it will be in short order.
The only short coming I see is if you would need this AC on muggy overcast days which are very common here.
What kind of AC is the unit? 1200w on a very efficient house (well done on R36) may actually be over kill. What’s the square footage?
One good thing to keep in mind is that if you start small, with say 100ah at 48v, and find you need more storage, plan the system around adding more storage down the road.
It’s very easy to add more so that your PV array is more “balanced” to the battery bank.
Actually I got the size wrong. I'm looking at
Midea Aurora Plus Smart Inverter Heat Pump 2.5kW, Chinese, one of the biggest appliance & ac manufactures, they sell under a lot of brand names, its all still new to me. Its as small as they come & dirt cheap, I guess < $500 us. Its unlikely I'd use the heater, as I cut my own fire wood & the burner heats water & has a cooking top, ideal for winter day temp ~ 10 - 15c, 50F - 59F , night -3c to 10c.
Sorry can't convert room size to ft, but I have a 10ft long hall with all the rooms connected ( so plan to install midway in the hall, which isn't normal), bedroom 40sqm, living room 50sqm. the
Heat Pump 2.5kW is suitable for a room ~30sqm. But I was thinking along the same lines as you with the batt & ac, start small & can expand if needed.
I have read a lot of post of people losing their batts due to a bad mppt fault, & batts are a huge if not the biggest investment here, that said I'm thinking of adding extra overcharge protection if possible to the b. bank, still researching. So I will increase the Ah over time.
As the
Heat Pump 2.5kW are cheap, if its undersize I can always add another directly to a room, but hopefully not, I should be able to direct the cooling by closing the doors on unused rooms etc (in theory). Still all guess work.
Thanks for your help.