How does the intake of carbonated water with sugar additives correlate with the incidence of cavities? Is carbonated water itself corrosive?
There is no difference between real and added sugar.
Glucose (C6H12O6) as an example can be an additive or a "original" nutrition of any natural product.
Carbonated water with sugar additives therefore has the same increasing chance of caries (and cavities) as the same amount of sugar as what companies might advertise as "Carbonated water with real sugar". Recent research has found that the amount of time spent consuming sugar has a larger effect on the risk of cavities than the amount.
This previous answer of mine talks about the corrosiveness of carbonated water and comes to the conclusion that
carbonated water might have a slightly larger effect on erosion of teeth than normal water because it is just a little bit acidic.
About sugar-sweetened beverages (SSB), the ingestion of 1-2 SSB daily increment the caries incidence at least in 31% (Source)
The use of carbonate drinks without sugar added increase the incidence of dental erosion (source).
Hence, any carbonated liquid is associated with dental erosion. If you add sugar, then is also associated with dental caries.