Solubility of CO2 in water at 0C and roughly atmospheric pressure is about 0.001337 mole fraction [0]. CO2 molecules are 44/18 times heavier than water molecules, so that's about 3.3g of CO2 dissolved in a liter of water. Carbonated water is usually specified in "volumes of CO2". One mole of gas at STP has a volume of about 22.4L, so one liter of CO2 weighs about 2g. "Lightly carbonated" is usually considered about two volumes of dissolved CO2, so 4g/L, which isn't much higher than 3.3g. Assuming the packaging is sealed well enough to maintain a high percentage of CO2 within, and the temperature is low enough, it looks plausible that there would be a noticeable change in taste/mouth-feel. This is confirmed by a study I found showing average taste threshold for dissolved CO2 in water of 0.26g/L [1].
One exception: fermenting liquids can become super-saturated with CO2 even if fitted with an air-lock to vent the CO2 to atmospheric pressure. This might cause a rather messy surprise if you add powdered yeast nutrient to an ongoing fermentation and give it a lot of nucleation points.
