I would never run a dry system in anything that didnt have EFI. Even then i'd be leery.
Wet system is when the nitrous is sprayed in to the intake along with a shot of fuel (2 separate jets). The reason pistons melt down in a dry system is because Nitrous Oxide is N2O. 2 nitrogen and 1 oxygen molecule. You are packing your cylinder full of extra oxygen. Although, N2O is in liquid form in the bottle, when sprayed, it quickly evaporates. This chemical reaction causes it to cool to about -120 degrees. It's not until it heats back up to around 600 degrees that the oxygen molecule separates from the nitrogen and is able to burn. In Nitrous Oxide form, the oxygen will not burn. By this time the cylinder is completely packed with extra oxygen and if you dont add fuel you will run incredibly lean and burn down the motor.
I dont see how injecting N2O into the airbox will make your carb meter for more fuel unless it's setup for a constantly intake of N2O (no button just on all the time). And if you ran out of N2O the bike would running super rich.