I've never bothered to figure it out, but it would be easy to do if you know the volume of the reservoir and plenum and used the data over multiple shots or a fill, and thus could work out the average usage per shot. We can work in "units" that define the amount of air used, pretty much normalized for pressure - I like "bar-cc" as that unit, and it is the volume of air multiplied by the pressure in bar. It is not perfect, as it treats the air as an ideal gas, but as long as we work under about 3500 psi it holds fairly true.
For example, I have shot string data handy on a double regulated bottle-fed Marauder I built that can show how easy the math is. It has a 480cc bottle on it, and a ~35cc plenum on a Huma regulator set at ~155 bar in it as the second one (the first is a Ninja in the drop block to smooth out the pressure to the Huma, but we can ignore that one as all shots are above the Huma set point). The math is straight forward . . .
On the 40 shot string, the bottle started at 3200 psi and dropped 950 PSI, or 65.5 bar. That give us 480cc x 65.5 bar = 31,440 bar-cc of air used over 40 shots, for an average of 786 bar-cc per shot.
As long as the pressure is above the regulator set point, the regulator will average holding 35cc x 155 bar = 5,425 bar-cc of air.
So on an average shot, the valve releases 786/5,425 or about 14.5% of the air it holds. That would put the low point of the pressure before the valve closes at ~133 bar. Of course this ignores the pressure drop across the valve and speaks only to the average value, but it gets you close.
Hope that helps. You can figure this out for any gun for which you know the volumes and data.