score:5
Quite aside from how you would picture a people not defending their country, there seems to be a significant misunderstanding here.
"The Cold War going hot" would not have been a war of West Germany vs. East Germany in which NATO / Warsaw Pact "might" have gotten involved.
Both NATO and Warsaw Pact had their forces stationed right there in Germany. So many, in fact, that the German forces were a minority. Significant, yes, but outnumbered by their respective allies.
The West German frontline was divided in to sections, which were defended by, in order from north to south, the West German / Danish Corps, Dutch I Corps, West German I Corps, British I Corps, Belgian I Corps, West German III Corps, US V Corps, US VII Corps, and West German II Corps.
Facing them from across the border was, likewise, not just the East German NVA, but formidable Soviet forces.
Neither West Germany nor East Germany would have been the ones to escalate things into a shooting World War III, which would have taken place on German ground, turning German cities into rubble.
But if things would have escalated into a shooting war, it would be difficult to imagine either Bundeswehr or NVA sitting it out while their allied armies would fight in their country. It would change nothing at all, the war would take place regardless.
Upvote:3
The Stasi considered large parts of the officer corps of the KVP/NVA unreliable (basically those who had already served in higher positions in the Wehrmacht), which is why they were sidelined in 1957. Note the proximity to the Hungarian Uprising of 1956. Case in point.
East German border troops were basically always suspected to be ready to go AWOL on the other side of the border. Which is why they were never allowed to be alone at the border and would also usually serve far from their hometowns (e.g. people from Berlin would serve at the inner-German border). Examples of border troops going AWOL and source for border troops being required to never separate from the other guy on duty.