I'd think we have to consider that not all East Germans supported their government. While the same could be said of West Germany, things like the Berlin Wall and the East German Uprising of 1953 prove this was more of a problem in the East.
If we set aside the fact that the war going hot meant world annihilation anyway, my assumption (based on attitudes on citizens in East and West), would be any type of conflict would be seen by a plurality as an opportunity for reunification and to rid itself of the relatively unpopular East German government.
The lack of support for the GDR was pretty much accepted fact by all sides, and the East Germans used that to their advantage to gain material support from the Soviets.
This situation provided the GDR with opportunities to convert its weaknesses into strength in bargaining with or manipulating the Soviet Union. The lack of popular support for the East German socialist government was manifested in the hundreds of thousands of refugees who fled to the Federal Republic of Germany (FRG) each year. The leaders of East Germany's Socialist Unity Party (SED) could, with justification, use the threat of the regime's collapse to obtain more aid from Moscow.30 In addition, as the weaker power, East Germany had more to lose, more at stake if it collapsed than the Soviet Union did and thus was more motivated and persistent in the pursuit of its narrow goals. This translated into increased bargaining strength.31