However check them after your jacks are down before you drive regardless.
I have checked them both ways before and never gave much thought to your hypothesis nor have I noticed much difference and evidently not enough to make a difference. Except one time when I checked with jacks down my inside right dually was flat. Had I dropped the MH and then checked I may have damaged the tires.
Checking them in the manner in which you are going to use the vehicle seems the right thing to do no matter whether you have checked them on the jacks or not.
Anyway it is a good question and we need an "air engineer" for some definition. It would seem logical that if you apply weight you increase the forces (pressure) in the tire. A balloon will break if you keep applying weight to it, is that a question of psi or volume?
Otherwise "why is there air"? (Bill Cosby sometime in the seventies).
I do all my own stunts
03 Dolphin LX 6355, Workhorse W22, 8.1 vortec, 04 CR-V, Blue Ox, Brake Pro----Norm, Barb and
Doc(He's a PhD)