In my application the liquid would be tapped from a fast-varying flowrate, and I want to measure the static pressure change during this by measuring the air pressure above it. Will this work?
Yes, the pressure will be identical (with some qualifications). If you think about it, the gas will compress until the force on the boundary between the gas and liquid are equal (i.e., the pressure). Even with a compressible liquid, this should also be the case. You will want to have a reasonable initial pressure for your gas, as well - it may not work as well if your gas volume shrinks to a very small size in response to a very high fluid pressure.
You will get some amount of gas dissolving into the liquid, according to Henry's law. I'm not sure whether that will be an issue with the fluid you are working with. The gas will evaporate out of the liquid / dissolve in response to the pressure increasing and decreasing.
How quickly the gas responds to the increase or decrease in pressure will be another question. It will depend on the gas you are using (based on whether it is monatomic, diatomic, molecular, etc - based on its capacity to store and release energy in various modes). It will also depend on the degree of fluctuation of pressure, as well as the temperature of the gas and the size of the volume pictured here. If either the gas or fluid are supercritical, or if the initial gas pressure is at a low vacuum, things will get weird, but as long as you stay within the regimes where ideal gas assumptions are relevant you should be fine.
One thing to note is that a big tap combined with a small chamber should reach equilibrium pretty quickly. You may want to be careful about getting into very high pressures though if you are designing the seals / shell for this pressure vessel. Using inert gases is obviously preferable. Additionally, if you're using a pressure transducer, you may want to fit it with a snubber to prevent damage from fluid hammer.