Hitler fought as part of German Sixth Army, a primarily Bavarian force that deployed first to the southern edge of the front and then later, in October 1914, to the area around Flanders and Artois. He was not a part of an Austro-Hungarian contingent on the Western Front. He was living in Munich when the war broke out in 1914. He later claimed, in Mein Kampf, that he wanted to join the German Army rather than the Austro-Hungarian Army because the latter was ethnically diverse (as it included non-Germanic Slavic, Hungarian, Romanian, etc. elements from all parts of the empire). In truth, though, it was simply convenient for him to join the German Army because he was in Germany. Hitler's military career is not my specialty, so someone else may be able to jump in here.

To answer your question, though, yes, there were some Austro-Hungarian forces were on the Western Front, but not many. Austria-Hungary was busy dealing with a messy war against Serbia, Russia, and later Romania.

The case I know best is of four batteries of Austrian Skoda 305-mm guns used against the Belgian fortresses of Liege and Namur in 1914. The Germans initially had some trouble cracking Liege. The army had commissioned Krupp to build massive 420-mm guns, but by 1914, only five were finished. Therefore, the Germans used the next best thing: the Austrian Skodas, a truly exceptional siege gun at the time.

The Skodas first opened fire on Liege on August 12, and within four days, its forts on either side of the Meuse were reduced (Strachan, The First World War, vol 1., p. 204). The Austrian batteries were then redeployed to Namur, where they fired 573 shells at the Belgian forts there between August 20 and 23. Prussian and Saxon forces stormed and captured the forts on the 23rd (Herwig, The Marne, p. 130).

There was also a token Austro-Hungarian infantry contingent sent to the Western Front in 1918. By this point, the war against Russia was over, but Austria had suffered heavily and was dealing with some major domestic problems threatening the survival of the empire, so there weren't many units to spare for the Germans' final push on the Western Front in March 1918. I don't have my reference source on hand at the moment (Herwig, The First World War: Germany and Austria-Hungary), but I believe the force was rather small and was defeated by French and American forces in the summer of 1918.