Can you push a liquid and a gas into a container at different pressures?
Pressure is due to the random impact of molecules on the surface, regardless of whether water or carbon dioxide or anything else. Once equilibrium is reached, all components are at the same pressure.

That said, there's no problem using a moving stream of $\ce{CO2}$ to propel and to mix with water at much lower pressure, using Bernoulli's principle. The automotive carburetor and spray atomizer operate on this basis.

The alternative, of course, is to add the water to the container through a check-valve, then add $\ce{CO2}$ at a higher pressure.

The choice is a continuous process vs. a batch process.