I know what you're thinking. It's a bit counter intuitive. Think back though to just about every diagram of a pressurized hydraulic/pneumatic system. You have a pump, an accumulator, a cooler, a pressure relief valve (the BOV) that returns pressurized excess back to the accumulator (ambient air in our case) and actuates a cylinder or turns a motor (the engine). Recall that relief valves return system volume to the accumulator and NOT system pressure.
So in the scenario above, where will the pressure drop be? So long as volume is supplied, there won't be a pressure drop. Air heats as it squeezes and accelerates, as soon as it expands again it slows, expands, cools rapidly and takes up less space per cubic measure than it did when it was hot.
If anyone recalls, the OLD discussions about the fuel rails were about why we were able to make so much more HP with 42 lb injectors and stock rails versus smaller injectors and FMUs (pumps were removed from the equation because both setups run the same pumps).
Anyway... Reminds me a great deal of sitting in hydraulic, and electro-environmental classes.