Does amp output V decrease by adding gain stage?

You can add as much gain as you want before or at the input of the amp but it will not change the amps output in any way. IOW whatever it is rated at in terms of full output wattage will be the same. What you will change is the sensitivity of the amp. IOW you won't need 4 volts to get the amp to full output.

Yes, adding a gain stage at the input would reduce the voltage needed. How much less voltage depends on the amount of gain that you add.