Short answer: yes.

The comparison between what became "East Germany" and what became "West Germany" resembles, on a long time scale and with a number of important qualifications, the difference between Northern and Southern Italy. West Germany, like Northern Italy, contains the majority of the commercial and industrial wealth of the country, while East Germany, like Southern Italy, was primarily focused on agriculture. Prior to the opening of the 19th century, this agriculture was performed by serfs in large tracts owned by nobles—this produced significant wealth for the wealth nobles due to the typically large size of their holdings, but left most of the population (including even the minor nobility) much poorer than their counterparts in the West. Prussia, the kingdom that controlled the majority of the land in what became East Germany, only abolished serfdom in the first decade of the 19th century.

Wealth in Germany has historically centered upon the Rhine Valley, due to the Rhine's role in moving goods through the Low Countries, and the fertility of the lands along it (which are fantastic for growing wine). In the medieval and early modern periods, the decentralization of the Holy Roman Empire and the many small, independent territories along the Rhine allowed many lords to make a reasonable amount of money charging custom duties to trade ships passing along the river. The weather is more temperate, the soil more fertile, and the area is more gifted with natural resources.

Northern Germany, particularly the parts which ended up in West Germany, also were quite wealthy at various points. During the era of the Hanseatic League, many cities became quite wealthy through trade. Most notable of these today is Hamburg, whose position along the Elbe River and excellent natural port have made it one of the largest shipping centers in the world for centuries.

Major source:

Thomas A. Brady, German Histories in the Age of Reformations, 1400-1650

It may also be worth noting that the parts of historical eastern Germany which were the most-developed and resource-rich, like Silesia and Koenigsberg, were permanently lost after World War II, making what would become East Germany a poorer region.