With denser, freer flowing air, less load on the crank/blower the charger will compress more "volume" of air into a "space" hence why the workshop who had no added ignition timing saw a rwhp gain from simply having colder, denser and more air at a lesser boost pressure.
So because the charger can push air into the "space" with more ease it can move more air volume into that "space"
so YES more air is being ingested and compressed as it's easier to put it into the pressurized "space" so blower efficiency is improved.
A reading of the air flow at the MAF will confirm the same and has previously shown more air passing the MAF.
View the air molecules as people, you can fit 100 fat hot sweaty people in the blower lid and cylinders however there is a line up of 10,000 more people outside waiting and pushing to get inside but because of the 100 fat people they can't fit inside there is no room as there is too many fat people.
If we shrink the hot sweaty fat people with freezing cold air to be cold hearted skinny people then we can fit a few more people in the engine.