Yes; both during pressure test and during operation.  During a pressure test, the gauge on my little battery powered air pump read 40 psi when air was escaping from the overflow bottle. Unless something else is happening, the pressures are additive.  The cap controls the pressure difference between what is under the cap, and what is downstream at the overflow.  The overflow from my filler neck cap connects to the overflow bottle.  When there is no pressure in the overflow bottle the system pressure goes up quite rapidly to about 23# as the engine warms.  As more coolant is forced into the overflow bottle, and that pressure builds, the system pressure increases.

 

I haven’t bothered to observe; but as the coolant temp drops, I expect the pressure drops quite rapidly to about the pressure that is in the overflow bottle.

 

Al