MG1 vs MG2 battery charging efficiency

MG1 I think only starts the engine (just like a conventional starter does).
In my view, it does not use gas. It only uses the energy from tour HV battery to get that done.
Where you get more gas being used is by the MG2.
That's the electric motor, that does the propulsion of the car.
MG1 would used more gas, if for instance, your HV battery is deteriorated already. That way, mg1 is always trying to recharge the battery, by constantly running the ICE.
Pls if my explanations are wrong, someone could pls, expatiate more.

 

MG1 and MG2 are both intimately involved in everything the transmission does. The flow of power in either direction between them (and it can flow in either direction, owing to the clever "overdrive" or "heretical" mode) is always part of the power flow between engine and wheels. The current into or out of the battery is best thought of as simply the net surplus or deficit between the two. Trying to think of it as coming "from" one MG or the other doesn't lead to a very fruitful mental model.