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Volumetric efficiency increases the more air you can get in to the cylinder, so yes, forced induction increases volumetric efficiency.
Unfortunately, to keep combustion chamber temps down and prevent detonation, gasoline engines usually pump extra fuel in that goes unburnt. The only real way (that I am aware of) to prevent the need for this is to inject the fuel immediately before it's to be ignited (direct injection). So, yes, some modern engines can be turbocharged and have higher compression ratios and are thus can be more efficient.
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