While technically true, I just can't see it making that much of a difference in SR or even in a gritty real life simulator. For the sake of argument, let's say the energy needed to cycle a M4 is equal to that to move the whole rifle 1 meter. That's 3.4 J (3.4 kg weight of a fully loaded m4 moved 1 meter). A 5.56mm NATO round has a muzzle energy of 1767 J. Subtracting it out, you get a muzzle velocity of 1763.6 J. A difference, yes, but a 0.2% one. There's just so many other random factors at that level that I can't see it breaking out of the noise. You likely wouldn't give a damage bonus for walking towards the target since your walking velocity increases the bullet's velocity and that's the scale we're looking at here*.
Bolt action rifles do typically use heavier loads than semi-automatic and automatic rifles. That's because the bolt action can handle higher pressures and thus are less likely to break when handling heavier loads. In addition, recoil is less of an issue as there's more time between firings.
*- Assuming a walking speed of 1 m/s (or 3.6 km/hr), the velocity will increase to 941 m/s. The total energy will then be 1771 J, an increase of 4J.