I got curious about this and decided to test it. I made a small scenario in the editor with three T34s and a German pillbox. The pillbox was put in the center of woods with no LOS so as not to influence the outcome. The scenario was 2 turns long. I ran it four times.
The first time I did nothing with the T-34s - German total victory because the pillbox got 300 points for holding the flag.
Next I drove a T-34 off of the friendly edge. Result: same.
Next game a drove a T-34 off of the neutral edge. Result: same.
Next game drove a T-34 off of the enemy edge. Result: same.
Conclusion: It makes no difference whatsoever what edge you exit your units off of. The score will be the same. Edges seem to only be important as far as which direction the men will run to when routing.
"Most sorts of diversion in men, children, and other animals, are in imitation of fighting." - Jonathan Swift