There is math involved. How much power you can put into the batteries and their rated capacity.

With our system [if we do not do anything], from 8am to noon, it can bring our batteries up to full capacity.

But if a load is in the laundry, or if I am melting lead and casting bullets, then our consumption of power will keep the batteries from being charged as quickly.

Also do not forget, that your system needs to be designed so you have a method of performing a monthly 'equalize' charge. It is a tripwire that manages to trip a lot of us.

It depends on the type of battery.
If it is Lead Acid (Pb) then you can typically only discharge it half way but you may need more than what you took out of it to charge it back to full.
If you are using a Lithium Ion chemistry you can use almost 100 per cent of the capacity and since Lithium batteries are 99 percent efficient you may only need a little more than you discharged to get it full again. In both cases it may vary because of inverter and charger efficiencies as well.
In both cases it is more complex than just hitting it will a high current charge. Again each chemistry has a maximum charge rate and then at about 80 percent full the current begins to taper off until the battery is full. There are some good stickies on batteries at the top of that section.

Thanks for the reply. It’s a lithium battery I am looking at ( Huawai Luna 5Kwh ). Are systems normally designed to give priority to one particular part of the set up? For instance, if my battery is fully discharged over night and then in the morning, when the sun gets up and the system starts to produce, will it prioritize the battery? If I switch something on, will it stop charging the battery and put the power into the house or will it keep on charging the battery and make up any shortfall by drawing off the grid until the battery is fully charged?

Every inverter has is own unique modes. The scenerio you outlined is very similar to one of the modes on my Outback Skybox. Another mode uses the grid as last resort.