Probation after six months (on the condition of good behavior) was already part of the original sentencing, so that required no special political pressure.
It was of course remarkable that Hitler and his posse got away with such a mild punishment - 5 years (which Hitler would have to have served without probation) was the mandatory minimum sentence for attempted treason (and the fact that several police officers got killed was not even mentioned in court). It was also remarkable that Hitler (who at the time was stateless foreigner) was not expelled from Germany (it was counted in his favor that he had served in the German military and considered himself "German"). The argument of the judge was basically that Hitler and company had acted with patriotic motives and in good faith ("in rein vaterländischen Geist und edelsten Willen").
So the release was not result of a direct political intervention, it was just that many people, including the judge, agreed with Hitlers goals, even if they were obliged to apply the law with regard to his methods.
This (German) page adds an interesting angle in that it says the judge had been chosen not mainly because of his sympathies for Hitler, but because he could be counted upon to protect the defendants von Kahr, von Lossow and von Seißen - all three were high ranking civil servants, and it was in the interest of the Bavarian government not to make their part in the coup too much a matter of public discussion.
Plus the NSDAP was declared illegal in 1923 after the attempted coup (and remained so until Feb. 1925). This does not suggest that letting Hitler participate in a democratic framework was a main concern.