I have no idea of what your asking on the intake valve pressure differences
I've dyno tested around 8 Roots blown gas motors, 3 hemi and several BB and SB Chevy.
The last pump gas Hemi (4.250 borex4.375 stroke and 9.3 to 1 mechanical compression ratio) made 924 HP at 7300 RPM with 130 F manifold intake temps. with 7.5 lbs. of boost with 12% under driven and 33 degrees BTDC ignition timing, we swap the pulleys and got 13% overdrive and put race gas in it and retarded the timing to 25 degree BTDC. with those changes it made 1027 at 6500 RPM with 12.0 lbs. of boost with 190 F intake temps and then went into detonation 30 minutes later after the best pull at 7.5 lbs. of boost
The dyno operator thought we took out to much timing so I bumped it up to 27 BTDC and it went into detonation at 6300 RPM 25 minutes later than the first pull with 12.0 lbs. of boost with more overdrive Stupid me
Looking back later I should have set the timing at 20 BTDC to start with on those changes with the increase boost
I didn't know how big the intakes temp would make compressing the air that much more Hot air expands, correct
The last N/A Hemi I built and dyno tested was a 572 C.I. with Holley dual dry 1150 CFM throttle bodies on a single plane Stage V inline intake and FHO CNC ported Stage V street heads, it made 799 HP at 6500 RPM on Oregon non ethanol pump swill.
My message is Roots super charger consume a lot of HP when compressing the air