I have never tried using ginger ale or any other soda in pizza dough but your question is an interesting one.
From what Canadianbacon and other Canadian forum members say, the use of ginger ale, 7Up and similar sodas in dough appears to be a Canadian innovation. Out of curiosity, I did a Google search to learn what is in Canada Dry ginger ale and especially how much sugar (whether corn syrup or sucrose). What I found as the ingredients are the following, for a 12-ounce U.S. can: Carbonated water, high fructose syrup and/or sugar, citric acid, natural flavors, sodium benzoate (preservative), caramel color. One can includes 33 grams of syrup/sugar, or 1.16 ounces. That converts to roughly 8.3 teaspoons of table sugar (sucrose).
To have a bit of fun, I wondered how the Canada Dry ginger ale might be incorporated into a typical dough recipe using 16 ounces of flour and calling for a typical hydration of 63%. That would mean about 10 ounces of liquid. If I assume that one fluid ounce weighs one avoirdupois ounce, then we would need essentially the whole can of soda to get to 63% hydration. (To do this accurately, one would have to weigh the contents of the can of soda and apportion between the water and sugar.) I estimate that the amount of sugar in the amount of soda needed to get to 63% hydration translates into a bit over 7.25 teaspoons, or about 6.5% on a baker's percent basis. Once you get above about 4-5% sugar in a dough, it is detectable by most people as sweetness in the finished crust. Also, above about 5%, sugar can degrade the performance of the yeast. One way to get around this problem is to just add more yeast to be sure that there is enough to perform its usual functions even in a degraded environment.
If I had to guess, I would say that at around 6.5% sugar, the finished crust using the ginger ale would be tender and have a lot of browning, and that color might even be augmented further by the caramel color in the ginger ale itself. At 6.5% sugar, it might also be wise to use a pizza screen or disk to bake the pizza, and not bake it on a deck because of the likelihood of premature or excessive browning due to the high levels of sugar. Maybe Canadianbacon or one of our other Canadian members can describe the crust for the pizzas they have bought from pizza operators who use ginger ale (or similar sodas) in their doughs. I'd be especially interested in the color of the crust, its sweetness level, and the size of the rim and the nature of the crumb. I'd also be interested in knowing how the pizzas are baked, i.e., on a screen, disk, conveyor or deck. The answers to these questions might even tell us whether the ginger ale is diluted with water to keep the sugar levels down.