I've rigged my model and have used the automatic weighting option. After rigging I've modified some bone's parent to get better deformation results. But, should I re-parent the rig after doing this? Testing it out it seems everything is fine. Or rather the question is: does the rig hierarchy order affect the automatic weighting results?
The rig hierarchy will not affect the results, you should only need to correct the weighting if you move the bone.
The mathematics behind this effectively first transforms each each vertex by each bone that it is weighted to, and then uses those weights to combine the transforms from each bone proportional to the vertex weight.