Non-equilibrium gas cap above saturated liquid-gas solution

If I could somehow instantaneously replace the $$\ce{CO2}$$ gas cap at the top of a soda bottle with a different gas, say $$\ce{N2}$$, would the bottle pressure increase as a result of the $$\ce{CO2}$$ de-gassing into the gas cap space?

I've come to this question because I am trying to design a method to measure the dissolved $$\ce{CO2}$$ content of a water liquid stream. The method involves exsolving the $$\ce{CO2}$$ into either an evacuated or $$\ce{N2}$$-charged vessel and measuring the pressure change to correlate dissolved $$\ce{CO2}$$. By Henry's Law the pressure in an $$\ce{N2}$$-charged vessel should increase as a result of $$\ce{CO2}$$ exsolving since the $$\ce{CO2}$$ partial pressure above the liquid is zero, should it not?

More clarification (hopefully) for those who have marked the question as unclear: Let's say I have a closed system (soda water in a bottle as an example) with a $$\ce{CO2}$$ gas cap at a pressure of 10 psig. The gas cap, like in a soda bottle, is small relative to the total volume, say 5%. The liquid (water) in the bottle is fully saturated with dissolved $$\ce{CO2}$$. Now let's say I somehow instantaneously replace the $$\ce{CO2}$$ in the gas cap with another gas, say $$\ce{N2}$$, at the same pressure (10 psig). The system is still closed (we've magically replaced that gas). Will the bottle pressure increase as a result of the $$\ce{CO2}$$ in solution exsolving into the gas cap space, since the partial pressure of $$\ce{CO2}$$ there is zero? This of course is hypothethical, but it would have some similarity to how the dissolved gas content of liquids drawn (pumped) from deep within a well could be measured.

Thanks

• Guinness beer will do. – Ivan Neretin Jun 11 '19 at 19:24
• Please see my updated description, thanks – prairieDog Jun 11 '19 at 21:36
• @IvanNeretin I had to look it up: allaboutbeer.com/man-invented-nitro-guinness – Karsten Theis Jun 11 '19 at 22:24
• To the point of the question: yes, it will increase. – Ivan Neretin Jun 12 '19 at 7:35
• Ok, thanks. Love the Guinness angle too... – prairieDog Jun 12 '19 at 14:05