Yes, of course.
The SA was used to terrorize political opponents; they originated from right-wing paramilitary groups that were abundant in Germany after the first world war. (The peace treaty limited the German army to a certain number (100000 soldiers); the German imperial army in the first world war was much larger and many units resented both the peace treaty and the new republic and simply refused to give up their arms.)
At first, the SA was used to protect Nazi-party events. (You are right, most political parties in Germany at the time had similar organizations for this purpose, the social democrats for instance had the Reichsbanner, the communists had the RFB etc.).
By 1923, as mentioned by @Tom Au the SA was used much more aggressively, however, forming the backbone of Hitlers first attempt to seize power. From the late 1920s, as the SA grew, there were more and more incidents of them openly terrorizing political opponents and thereby unlawfully influencing the political process; consider this murder of a German labor union activist as an example (unfortunately only in the German and Italian wikipedia).
Note that the SA was illegal during parts of the 1920s and the early 1930s - the German authorities realized, of course, that they were a threat. However, as substantial parts of the German burocracy, and substantian parts of the political and economic elites supported the right wing (and from a certain point on specifically Hitler), this did not last long. They played an important part in Hitler's consolidation of power in 1933. Many of them were briefly given official status as auxiliary police force; having already influenced the voting process in the elections in February 1933 (having been ordered to "monitor" them), they then prevented the seating of elected left-wing MPs in parliament.