What happens if bread is made with sparkling water?
I am not a chemist, but my grandma always used to make bread (and similar stuff) with sparkling water instead of still water. She always mentioned that the result will be more fluffy and airy. This only addresses the question about the (important) consistency though, but I guess you should just try it out yourself.

Edit:

Some benefits of using sparkling water in the kitchen

As this answer got downvoted to zero I guess my grandma was not convincing enough. So I asked a befriended chef who works at a luxury hotel chain in Germany. Here's what he explained:


Desserts can be made more creamy without actually adding cream. Here he gave examples of pudding/mousse-ish desserts
Vegetables steamed with sparkling water results in less loss of color (i.e. brighter colors), more crispyness, and stronger taste. He particularly recommended to try it with carrots, broccoli or cauliflower.
You can add sparkling water to thick soups shortly before serving to get them more foamy. 
Similar with Salad dressings
Last but not least he confirmed precisely what my grandma said. For doughs and similar stuff (for salty or sweet dishes) you would get a nice fluffy texture. Kudos to my grandma at this point.