As long as you can continuously get the CO2 out of the way above the surface so you don’t suffocate… you might still die.
“Non-buoyant water” is a real thing. When water contains enough dissolved or finely dispersed gases, it becomes less dense than the human body. There will be no buoyancy force making you float, so if you stop moving you won’t just hang near the surface, you will sink to the bottom like a rock.
Now, maybe you can still generate enough force to tread water if you really tried. Maybe the bubbles themselves getting caught under you would counteract the loss of buoyant force, but the point is that if you carbonated a pool enough, it could possibly be more of a deathtrap than a play area