CO2 and water are in an equilibrium. One in a thousand CO2 molecules will form carbonic acid with water. If the dissolved CO2 has escaped, the equilibrium has that many less CO2 molecules to play with, so one in a thousand out of much fewer CO2 molecules will form carbonic acid now. The carbonic acid that already exists, will escape after burping (equilibrium, remember?), but it can take a few minutes - equilibrium can be attained within 5 minutes. But this time is insufficient to get the carbonic acid to be absorbed into your bloodstream.
Unless you are a super pressurized container, carbonic acid remaining in your gut is a very small fraction of what you are creating through respiratory/metabolic process when you are "active". 4% of all your exhaled air could be CO2 - a litre of cola pales in comparison.