Since this is such an absurdly specific question I tried to do a little bit of reading to see what I could come up with.

In German Democracy : From Post-World War II to the Present Day Gert-Joachim Glaessner writes that the idea of drugs, as an example of a decaying or corrupted society, were often used as a tool by the GDR in opposition to the FRG. He says that

The leadership never tired of stressing the social security in which GDR citizens could live, in contrast to the unemployment, material want, and other problems of capitalist society, such as crime and drugs.

He doesn't go into detail on that claim, but I think we can surmise that if the GDR state didn't like it, it was unlikely you were going to be doing it unless you really wanted to stick it to the authorities or were in a very priveleged position. The Stasi were not known for their relaxed attitudes toward law-breaking, especially if it makes the GDR look bad, in their eyes, compared to the FRG.

In "Youth Justice in Germany" Hans-Jörg Albrecht claims that there were distinct jumps in crime in East Germany - including cannabis offences - following reunification, to a far greater extent than in the west. He gives a number of theories for this;

Some argue that young people in the east are far more exposed to risks thought to contribute to crime and therefore are far more involved in crime-particularly street crime and car theft (Frehsee 1995; Kerner and Sonnen 1997, p. 342).
Police and the public in the east may also still differ from the west in control styles and crime reporting patterns.
Another hypothesis is that children and juveniles in the east are far more visible than in the west because the infrastructure of specially designated places for juveniles is only slowly catching up with the west.
Another hypothesis, not yet examined closely, is that extended group activities (which produce more suspects for a single criminal offense) are more common.

He's more of a sociologist or criminologist than a historian, but it doesn't mean his views aren't valuable. Note that he is talking about both pre and post unification here though, so it's not all that valuable when you're talking specifically about the GDR. It just provides a bit of insight.

From these limited sources I'm going to go out on a limb and say marijuana didn't really figure in the minds or needs of the people of the German Democratic Republic. Certainly not enough for there to be a distinct cannabis culture or "problem" if you want to frame it that way.