chriso, I don't want to bore you but the math is fairly simple.
1 minute of angle (MOA) = (2 * PI)/21600 radians
This is because there are 360 degrees in a circle, and each degree contains 60 minutes of angle. So there are 360 * 60 minutes of angle in a circle = 21600.
Now, for a circle, S = r * theta where S is the length of the part of the circumference between two radial lines of length r separated by an angle theta in radians. 360 degrees is 2*PI radians = 3.14159 * 2 = 6.28318 radians. 6.28318/21600 = 2.9089 x 10^-4. So each MOA is 2.9089 x 10^-4 radians. So at 100 yards, 1MOA = 100 yards*36 in./yd*2.9089 x 10^-4 radians = 1.0472 inches. So 1/4 MOA = .25*1.0472 in. @ 100 yards = 0.2618 inches. So to figure out a 1/4 MOA adjustment at 200 yards you need to do the following.
1/4 MOA adjustment (@ 200 yards) = 0.25 * 200 yards * 36 in./yd * 2.9089 x 10^-4 radians = 0.5236 inches
So the short answer is ... NO, a 1/4 MOA adjustment at 100 yards will NOT produce the same results as a 1/4 MOA adjustment at 200 yards. However, the good news is that the relationship is linear so if you know what a 1MOA (or 1/4 MOA) adjustment does at 100 yards, just multiply the effect by 2, 3, 4, 5 etc for 200, 300, 400, 500 yards.
Here's a question for you ... what would a 1/4 MOA adjustment do at 50 yards?
Note: We've all heard of, seen or used the formula to calculate the circumference of a circle:
C = 2*PI*R where C is the circumference of the circle. This is the same as S = r * theta. In this special case, S is the circumference, r is the radius of the circle and theta is 360 degrees which is 2*PI radians.