Most CO2 that is used to make soda is purchased from other sources, where it is a byproduct of some other process and would normally be vented into the atmosphere. So really putting it into soda, then opening the soda to release it, produces a net effect of 0.
Even if the CO2 was somehow created just for soda, the emissions would still not be very great. It's calculated that CO2 from soda in America, the world's biggest soda drinker by far, would amount to only about 400,000 tons of CO2 per year--or about what a single 1000 MW coal power plant would generate in just over 2 weeks.
It's like a drop in a giant lake.