My initial gut reaction is that it probably won’t, because traditional pizza crust is a kneaded, heavy dough (relative to batters and very light pastries), two qualities that make it unlikely for the effervescence of the water to do much good. 

By the time you’ve let the yeast wake up to start fermenting, added your other ingredients, and mixed and kneaded the dough, my guess is that those tiny little bubbles are going to be long gone.  Carbonation is helpful in making lighter tempura and beer batters (as in our fish & chips recipe), as long as they’re used immediately, but I don’t think it’s going to provide much leavening to an actual dough.

The only reason I can think of that it might give you a crispier crust is that you’ll be adding slightly less water if measuring by volume, due to the space taken up by the bubbles, and less water can lead to a stiffer crust.

That said, I don’t have personal experience with this substitution to tell you one way or the other for sure.

- Question Submitted by Lonnie