That's not the main problem
I had made many threads about east germany, and in every of them a single major issue happens: The eastern germans saw their country as a soviet occupation zone, they hated their government, and as soon the soviet government became unable to slaughter the opposition as they did in 1953, the DDR fell, here one of the comments I saw:
So it seems that in case of war, the eastern german army would be fighting not only against the NATO, but also against a massive internal unrest