There are two different schools of thought on this.
There is the empirical, measure groups at two locations to see if there is a change group, and they have found using screens that MOA doesn't change with distance.
The other group is the "yaw stability" group and they show that bullets do increase in stability during time of flight.
Personally I've had loads that didn't group very well at 100 (right at 1 MOA) go into a 1.5" group at 200 (0.75 MOA) rather consistently. This led me to believe that after the initial yaw instability of my bullets was overcome by aerodynamic forces, that it would be a 0.75 MOA group at pretty much all distances up to the transonic zone (when weird things start happening to some bullets).
That is just my experience, using a 308 Win and 168gr HPBTs. The article I read about using screens to measure MOA at multiple distances for the same shot group was using a benchrest rig if I recall correctly. Benchrest bullets are known for very good imbalance and stability even at short range.
Machine guns are awesome until you have to carry one.