First, regarding general health effects of carbonation, in their 1992 paper Lambert et al compare re-hydration after exercise for carbonated and non carbonated beverages. The paper measures blood plasma levels prior to dehydration and after the administration of test solutions concluding;
A major finding of this investigation
was that fluid replacement was similar
in the carbonated and non-carbonated
treatments. ... the similar plasma
volume and total plasma protein values
at all time points suggest that
beverage carbonation did not
measurably alter the availability of
Also, Cuomo et al investigate the effects of carbonation on digestion, concluding
In patients complaining of functional dyspepsia and constipation, carbonated water increases satiety and improves dyspepsia, constipation and gallbladder emptying.
Which may explain why many people use sugarless carbonated beverages (such as sprite) to calm upset stomachs.
Also, a particularly interesting paper by Simons et al investigates the oral sensation associated with carbonated beverages, arguing
carbonated water excites lingual
nociceptors via a carbonic
anhydrase-dependent process, in turn
exciting neurons in Vc that are
presumably involved in signaling oral
Regarding kidney function, beverages with high fructose content may pose a risk whether carbonated or not. Studying rats, Gersch et al find an association between fructose and kidney problems.
Next, El-Badrawy et al touch on a distinction between 'cola' and 'un-cola' beverages, finding histopathological effects (I needed a quick wikipedia to understand this refers broadly to tissue damage) from colored soft drinks only.
The kidney of rats consuming dark
color soft drink showed congestion of
interlobular homogenous proteinaceaus
casts in some renal tubules (Pict.7).
While the kidney of rats consuming
orange color showed the previous
changes with congestion of the
glomerular tufts (Pict. 8). Kidney of
rats consuming colorless soft drink
revealed no histopathological changes
(Pict. 9), meanwhile, kidney of rats
consuming mixed soft drink showed
vacuolation of endothelial lining the
glomerular tuft together with
necrobiotic changes of epithelial
lining of some renal tubules (Pict
Like the original poster, I had trouble finding a credible source clearly attributing health impacts to one or more ingredients in soda individually. Many papers unequivocally argue soft drinks are harmful to health generally, but parsing out the effect of carbonation seems more difficult.
Even in a randomized setting, isolating the effect of one substance consumed in tandem with many others poses a challenge. Also, though similar in many ways, humans and rats differ. With these caveats in mind, the research outlined above seems to suggest the primary health risk associated with cola may be attributed to sugar content. That said, none of the literature I reviewed affirmed the negative, i.e. ``carbonated water does not impair kidney function''.