I answered a similar (since deleted) question some time ago, so I'll draw on that a little bit here.

The answer to your question is "no," which is perhaps unsurprising, since in history universals ("everybody was doing this"; "nobody did that") are rarely, if ever, true. The protests in East Germany in 1989, which led eventually to the fall of the Berlin Wall on 9 November, took many forms, involved many different groups, and expressed many demands. Reunification was not the primary demand. In fact, it was not even on the protesters' agenda until after the Wall fell. The transformation of the East German protest movement from a movement for reform into a movement for reunification was, for many participants, actually a tragic co-optation and transformation for the worse. Reunification was not only something they weren't demanding: It was something many of them actively opposed.

We have a great understanding of just what the protesters wanted, because they wrote it all down in legal publications and in the illegal or questionably legal samizdat, because they were recorded talking about it at public rallies, and because so many of them are still alive and still talking about it.

(Sidebar: I am going to refer to these people as "the protesters" for ease, but I should mention that while there were some massive public protests in East Germany in 1989 - for example, Berlin on 7 October and 4 November, Leipzig on 9 October - I mean to include all groups who played a role in the "resistance," however slight, to the SED dictatorship. This includes people who marched, people who wrote, people who fled the country, etc. It's a large group, including at least hundreds of thousands of people. Numbers of attendees at protests are always approximate, but the common estimate of "at least half a million people" showing up to the Alexanderplatz demonstration in Berlin November 4 indicates that about three percent of the population of the GDR was there. If a proportionately large protest occurred today in Washington, D.C., more than nine million people would have to be involved.)

What did the protesters want? One of the best distillations of pre-November demands came from a group called the "New Forum" (Neues Forum). The New Forum was created in September of 1989 to serve as an independent and legal body for organizing political reform protest in the GDR outside of the protestant churches, which had up to that point been the primary shelter for protesters. At the outset, they articulated their demands in a document they called "Awakening '89". Here's a relevant excerpt from an English translation:

We want leeway for economic initiative but no degeneration into a dog-eat-dog society. We want to keep the proven and yet create space for innovation in order to live more economically and less harmful to nature. We want well-ordered conditions but no paternalism. We want free, self-confident people who nevertheless act community-conscious. We want to be protected against violence and thereby not put up with a state of bailiffs and police spies. Lazy bums and braggarts shall be removed from their influential positions but at the same we do not want disadvantages for the socially-deprived and the helpless. We want an efficient health care system for everyone but nobody shall malinger at the expense of others. We want to participate in export and world trade but neither become a debtor and servant to the leading industrial nations nor become an exploiter and creditor of economically weak nations. It requires a democratic dialogue about the tasks of the constitutional state, the economy and the culture in order to recognise all these contradictions and to listen to and to evaluate opinions and arguments and to differentiate general interests from special ones. We have to think and talk to each other about these questions in the public, together and in the whole country. Whether we find ways out of the current critical situation will depend on the readiness and the desire for that.

Three things are worth noticing here. First, the demands are articulate and detailed, drilling down into specific (if implied) failings of the East German system, like pollution, the inefficiency of the healthcare system, the GDR's foreign debt load, and the domestic spying activities of the State Security apparatus. Second, the demands are more-or-less in line with mainstream democratic socialist (or even social democratic) ideas about how an ideal state should function: A balance of freedom with "community consciousness." This is, to be sure, different from the state ideology of the GDR, but not that different. And third, nowhere is the idea of unification with West Germany even mentioned.

New Forum was not an outlier here, either. Ingo Schulze, a dissident writer, described his experience of 1989 thusly (link in German, my translation):

"Visa-free all the way to Shanghai!" From the start, it was about the whole world! And it was about authorization of the New Forum and new parties, about access to the media, about free elections and above all about democratizing our own world. The call "we are the people!" was the decisive watchword. It was actually about taking our country into our own hands. In factories, schools, universities, theaters, and institutes, those who held the trust of the majority had begun to be elected to leadership positions. That was the real revolution. Who could stop us? With every new day, the the realization of a 'socialism with a human face' seemed ever more inevitable.

"Our own country"; "our own world"; "our own hands"; "socialism with a human face." For Schulze, as for others, the experience of 1989 was one of demands for change at home, which only later became demands for the reunification of Germany. There was even hostility among the protesters toward people motivated by a desire to leave the country. In Burning Down the Haus, his history of punk rock music in the GDR, journalist Tim Mohr describes conflicts between reformists and so-called Ausreiser, people who wanted to leave the GDR for the West:

Naturally these people did not share the same goals as the fighters. Many of the Ausreiser just wanted to be photographed by the Stasi while taking part in any sort of anti-government activity, in the hope that it would help their chances of being allowed to leave the country. In other words, the would-be emigrants were narrowly self-interested, reckless, and in essence apolitical. And they were starting to create headaches for those who sought to fight the dictatorship rather than run away from it.

(Continued in a comment below.)