The flywheel has no impact on emissions.

A turbo kit, properly tuned, should pass an emissions inspection just fine.

Emissions tests sniff for carbon monoxide (CO,) hydrocarbons (HC,) and oxides of nitrogen (NOx.) Different levels of each can indicate different problems. The visual protion is just that... looking to see that the emissions equipment is all there. All they are really looking for on a Civic is the catalytic converter.