I can't really go so far as to say 'no, absolutely not' because there may well be some counter-example lurking in the archives somewhere - I've flicked through a few places where such an individual might be mentioned, and found nothing. But we can at least say that it was highly, highly unlikely for any number of reasons.

If you were a German in Spain, your life was likely to be following a particular kind of trajectory. The vast bulk of German volunteers did not depart for Spain from Germany - they tended to already be in exile, members of leftist political organisations or racial categories for whom Nazi Germany was a dangerous place to be. Some had been forcibly expelled from Germany: arrested, imprisoned, stripped of citizenship and exiled. They had congregated in places like Switzerland, Prague, Paris and Moscow, alternately plotting the end of the Nazi regime and fearing the long arm of its security forces. Spain, for these individuals, represented a place in which fighting back finally appeared possible, the continuation of a struggle which had been lost violently and suddenly at home in 1933.

For those who survived the war, what to do next was an acute problem. Few countries were willing to welcome them - they were proven radicals, after all, whose politics were at odds with most pre-war nation states. Those that were more willing to host them, such as Mexico, were far away, and few could afford the journey. For those best connected to the international communist movement, Moscow was a viable safe haven, though hardly a safe one given the extent to which Stalin's paranoia of foreign spies and interference had led to the decimation of what had been a vibrant internationalist scene based around the Comintern for much of the 1920s and 1930s. For those with impeccable communist credentials and demonstrable loyalty, such as future DDR leader Walter Ulbricht (who spent some time in Spain, but as a political representative rather than a fighter), it was however possible both to survive and eventually emerge as a powerful figure in postwar Germany.

In the months after the fall of Catalonia in early 1939 (where most remaining foreigners had been concentrated, and from where flight over the French border was possible), those that could take these options of emigrating to a neutral country or to the Soviet Union did so. For many others, this was not possible - they were interned amongst tens of thousands of Spanish Republican refugees in vast camps in the south of France. While other volunteers in a similar predicament (such as some Americans and Canadians) were eventually released to their home states, there was no question that these men and women would be immensely unwelcome in Nazi Germany, and few would have wanted to risk returning anyway. Thus, they languished, even after the outbreak of the Second World War.

The Fall of France in 1940 changed their position suddenly. Some managed to escape the camps, joining the Resistance or fleeing the country as best they could in the chaos. Many others weren't able to escape though, and found themselves once again under the power of the Nazi regime. The most common fate of the former German volunteers in this situation was deportation to concentration camps such as Mauthausen in Germany. These, naturally, were not pleasant places to be, though they did afford the volunteers some opportunities to integrate themselves into camp political networks, where their status as Spanish veterans gave them some standing, and many managed to survive the war in the end. There was, however, no question that they would be joining the Wehrmacht - they didn't want to, and they weren't wanted.

Josie McLellan gives a useful breakdown of the various trajectories that German IB veterans had through the Second World War, though I'd note that the sample (the c. 1000 IB veterans who had chosen to live in East Germany after 1945) means that it's somewhat skewed. Nonetheless, it gives a sense of what happened to them collectively, indicating not just how varied and scattered these experiences were, but also how far they simply didn't include 'living a "normal" life in Germany":

Statistics collated in the GDR give an impression of where the veterans who later returned to the Eastern half of Germany spent the war years: 34.5% in Nazi imprisonment within Germany; 17.4% in the French resistance; 15.9% in the Soviet Union; 2% in Switzerland; 1.9% respectively in Sweden and Mexico. Other veterans spent the war in Denmark, Czechoslovakia, China, England, Chile, Argentina, Belgium, the USA, Holland, Columbia, and Greece; 2.8% remained in Spain in Nationalist captivity, some of whom were not be released until 1946.

This doesn't negate the possibility - someone who fought for the Wehrmacht in these circles would obviously not be eager to disclose that fact, and anyone who genuinely had changed sides after 1939 would hardly have chosen to stick around in or return to East Germany. I would not be at all surprised if there was some very weird life stories that emerged from Spain, and that could plausibly include fighting for the Nazis (indeed, there's some lingering controversy surrounding Irish Republican Frank Ryan, who was a dedicated anti-fascist in Spain but at least went through some motions of collaborating with the Nazis against the British during the Second World War). For the German volunteers, however, it would be incredibly atypical.