Fertilizer is commonly rated with an NPK ratio. The P stands for phosphorus (technically, P2O5), and it is the amount (percent by weight) of the fertilizer. So in a bag of fertilizer that is rated 4-10-6, the amount of P2O5 is 10% w/w.
The amount of phosphoric acid (H3PO4) in coke (original = 0.089%) (zero = 0.147%), and (vanilla = 0.147%). Source.
Pound for pound, H3PO4 has less phosphorus than P2O5... and since sodas like coke have a relatively minute amount of phosphoric acid, the calculations (comparing it with fertilizer) are beyond trivial. Coke/soda is nothing like a fertilizer.
The amount of carbon dioxide is about 2.2g per 355ml soda (source). As we all know, plants consume carbon dioxide; so for what it's worth, compared with humans, that's about 48.6 breaths' worth of CO2.
Calculated from 2.3lbs CO2/day (source) and 23,040 breaths per day (source)...
2.3 lb = 1043.1g
2.2g x (23,040/1043.1) = 48.6 breaths
However, soda also contain a fair amount of sugar (about 10% w/w) (source) so pouring it on a plant will likely incite bacterial and fungal growth (which would not be very healthy).