It's probably the least understood part of Hitler's life, actually. He did serve the revolutionary government and the Soviet Republic in some capacity, though perhaps not enthusiastically since he had already voiced his distaste for Social Democracy by then. He of course had no interest in letting any involvement become widely known later in his life.

Ian Kershaw has the following to say in his seminal biography:

Since the Munich garrison had firmly backed the revolution since November, and again in April supported the radical move to the Räterepublik [Soviet Republic], the obvious implication must be that Hitler, in order to have been elected as a soldiers’ representative, voiced in these months the views of the socialist governments he later denounced with every fibre of his body as ‘criminal’. At the very least it would appear that he could not have put forward strongly opposed views. Already in the 1920s, and continuing into the 1930s, there were rumours, never fully countered, that Hitler had initially sympathized with the Majority SPD following the revolution. Since the rumours tended to come from left-wing journalists, seeking to discredit Hitler, they were presumably not taken too seriously. But comments, for example, in the socialist Münchener Post in March 1923 that Hitler had assisted in the indoctrination of troops in favour of the democratic-republican state match the evidence, which we have noted, that he served, probably from February 1919 onwards, in such a capacity as Vertrauensmann of his company.

R. H. S. Stolfi, in Hitler: Beyond Evil and Tyranny, points out that Hitler's election to this position may not have been evidence of any opportunistic embracement of Marxism, but simply a consequence of the respect many of his comrades in his regiment felt towards him -- and he simply did what he felt he had to do in the circumstances.

I'm not aware of any further conclusive evidence having been brought to light on this point.

The bottom line, in any case, is that it was a strange and disorienting moment in Bavarian and German politics. A number of later Nazis supported the Bavarian revolution and even the Soviet Republic.