A No he did not: the Berlin Summer Olympics were held in 1936 and Adidas were registered as a company in 1949. Adidas were founded by Adolf Dassler, but prior to the registeration of the company, he owned and managed the 'Dassler Brothers shoe factory' with his brother Rudolf. Jessie Owens wore shoes produced by the Dassler Brothers factory at the Berlin Games. So, while he did not wear Adidas shoes at the Berlin Games, he did wear shoes designed by the founder of Adidas.
Jessie Owens competed for the United States of America at the Berlin Games, and won the gold medal in the following events: 100 m, 200 m, 4×100 m relay, and Long jump. Owens was the 'star' athlete of the Berlin Games, and is historically relevant because the Berlin Games were held when the Nazi Party governed Germany and Adolf Hitler attended events that Owens participated in. In 1935, Jessie Owens set three new world records in 45 minutes, and it is regarded as one of the greatest feats in modern sporting history.