Can you inject carbon dioxide/nitrogen into a dough/batter to provide leavening? Or use dry ice/liquid nitrogen?
It is not uncommon to use an ISI whipper for this purpose.  For example, tempura batter can be placed in a whipper, and it can be charged with CO2.  I'm not sure if that is more advantageous than simply mixing rice flour with seltzer water, but it is done.  Liquid nitrogen would freeze your batter, as would dry ice.  Dry ice would leave your batter somewhat carbonated upon thawing.  Your approach likely depends on what you are trying to accomplish.  I don't think this would be an effective approach dough, and for baking.  It might make sense for some batters.