assuming you mean direct injection if you don't cool the air coming in surely you cant get the same VE as a system the injects proportion to airflow (and not on the walls) that maximise latent heat of vaporisation to cool IAT to fit more mass in the cylinder. direct injection once the air is trapped well its trapped, the fuel can still cool to improve knock resistance but not improve VE. there may be some improved chamber temp that improves VE for the next cycle but IDK
clearly from a fuel economy and emission DI is better otherwise OE wouldn't do it but for max effort i'm not sure DI is the answer.