Ok got to weigh in here.
Almost NO WW2 aircraft were turbocharged, the technology of turbine materials wasn't well known at that point so it wasnt reliable enough at that stage. Plenty were supercharged, (ROLLSROYCE MERLIN,DB v12, bristol etc) but only a couple were turbocharged (Wright Cyclone, Allison 1710) and centrifugally then.
The statement above about VE was correct, boosting the pressure on the intake is about VE only.
Dont compare a Diesel engine to a petrol one, they are a completely different animal.
A Diesel is a compression ignition engine where the combustion is stratified, thus there is no lean mixture in the sense of the petrol engine, the small ball of fuel right at the injector inside the cylinder is the right mixture to burn, the fire once lit is added to as the combustion continues, all of the fuel isnt in the cylinder when combustion starts, adding more fuel just makes the fire bigger.More fuel equals more heat which equals mor pressure equals mor torque. The Diesel operates always with "excess air", that is ,its always got more air than it needs to support complete combustion, even when not blown, this is part of the reason why the exhaust temperature is lower and a NA engine never has the power of a similar sized petrol engine.
Adding a correctly matched turbo to a Diesel usually improves its thermal effiecncy as some of the waste heat of the exhaust is recovered to improve combustion.
NB a "gas" engine to me runs on a gaseous fuel like Methane or propane.
Most Diesels are not throttled in any way, a lot run VERY high manifold pressures eg up to 500kpa. They also do not suffer from combustion knock, so as long as the engine can stand the thremal and pressure loads you can keep increasing the MAP. Some C15 caterpillars have 300kpa boost. They get good life and reliability in average service, down here in Australia they do blow up from time to time, we generaly haul much heavier loads than the USA and in very high temperatures. 42-48c.
Back to petrol engines, generally the turbo or blower is added to increase VE, it generally does not improve thermal efficeincy in any way, usually makes it worse. So thats why there arent many turbo petrol engines in use, SAAB tried smaller turbo engines to try and improve fuel effiency but didnt get a lot out of the excercise. The whole trouble is because the petrol engine is a homogeneous charge, so they cannot be run any leaner than the lower combustable limit, the fire simply goes out.
Overall if your attempting to improve fuel effiency, get a Diesel, a small direct injected turbo Diesel like a Duetz.
My two pence worth
A7M