It wouldn't... as the firing pin merely strikes air in a centerfired rifle [or pistol]
If dryfiring is a form of active practice...why has the military then spent millions for range ammunition?
It is a little more complicated than that. There is a such a thing as snap caps. That is what LHO was doing when he used the CE 543 as a shell so that the firing pin would not break. A carcano firing pin is prone to breaking because it has a tapered shoulder that that strikes the bolt face if it is over extended during dryfiring.
The marksmen chosen to fire the Carcano for the WC chose not to practice dry firing the rifle for fear of breaking the Carcano's firing pin.
CE 543 shows the marks on the shell casing that it was used as a snap cap by LHO. That was the observation of Dr Chapman when he examined the shells and noticed the dished in primer. To recock the carcano to dry fire with it, the only movement that is needed is to raise then lower the bolt. That motion recocks the firing pin. Unless Marina stood there and watched LHO work the bolt she would not have known he was practicing trigger control.