To begin,in my head from draft angle days,a degree is about .017+ thousandth of an inch,per inch.
Just to illustrate the math,doing it in our head,lets call it .016 thou per in.
Now,just for this example,lets make the ring spacing 4 inches.
What would a .001 lateral or vertical error do to POI?
Well,.016 per in would be .064 over 4 in for 1 deg.As there are 60 MOA per deg,64 thousandths would translate roughly to 1 MOA per .001 error in ring to rail variation.
The design of the picatinny rail is quite similar to machine shop fixturing.
If the surfaces are accurately machined,clean,and have no burrs ,dings,casting roughness,etc they should repeat postioning to way less than .001 .That is a big "IF".
There is another issue.Alignment.If the scope rings are not perfectly clocked to the same orientation on the tube,tightening the rings to the base makes the scope tube a torsion bar.That introduces variability.Tightening the ring clamp screws can easily introduce this error.
Two piece bases?.Unless you have set up on a granite surface plate with a test indicator and confirmed alignments,do not assume the front and rear bases and the rings will all come into alignment.If they are not coaxial,tightening the rings to the bases involves flexing the scope tube.
This "springy" stuff makes repetition tough.
I thinkif you have a flat,true,rigid rail,such as on a quality AR upper,and you use a quality one piece ringmount,that is precisely CNC machined,
so that clean,non stressed surfaces can come together,repeatition will be very close..Should be easily sub MOA.