Yep, you are Lee.
12V is 12V is 12V and the type of battery chemistry or Ah rating won't affect the hybrid side at all, or at least not in the context that you're thinking. A brand new battery should be fully charged or not far off, so it shouldn't take much to bring it up to full and keep it that way.
The combustion engine will still fire up to keep it charged up as and when it needs to, but it won't be any more or any less frequent just because you put a larger capacity battery in the car. There will be a lower voltage threshold that will trigger the engine to come on and a higher voltage threshold when the engine will turn off and those values won't change depending on the capacity of the 12V battery.