Yes, absolutely. Initially, the camps were primarily for the punishment, ideological "re-education" and isolation of prisoners. Prisoners were assigned work as a way to recoup some of the costs of maintaining prisons but there was little organization and the work they did wasn't particularly useful, mostly tree logging and such. Gradually - and this idea was pushed through by a former prisoner of the camps, a man named Naftaly Frenkel - the authorities recognized the economic potential of using forced labor and reorganized the camps into what resembled commercial enterprises designed to be economically productive and sustainable. In fact, it wouldn't be too much of an exaggeration to state that the economic output of the camps was their primary purpose as the Gulag system evolved.

Starting in late 1920's, prisoners were put to work on massive projects all over the country. In the northwest, the White-Sea-Baltic canal - a major water way linking the Baltic Sea to the Arctic Ocean was built almost entirely using gulag labor. Further to the east in what is today Komi Republic, the Soviets built a system of camps for coal mining. Further east, they built the city of Norilsk to be one of the largest nickel mining and processing operations in the country. Farther west still, near Kolyma river in Siberia, the Soviets had built a system of camps for gold and diamond mining. To support these operations in the high arctic, they also needed to build roads and other infrastructure to connect the remote camps to the rest of the country.

The focus on maximizing production became even more stressed when Lavrentiy Beria, the head of NKVD and several other agencies in the USSR, took over the leadership of the Gulag. For example, camp managers received strict quotas on their production. Moscow administrators pushed to improve the conditions in the camps - less for humanitarian reasons but more because disease, malnutrition and overwork took toll on the bottom line. The local camp mangers faced enormous pressure but also were sort of like the Soviet equivalents of business magnates, with their own mini-empires. Some even had their own soccer teams and theater productions - all from prison labor, of course.

At their height, the camps contributed close to a quarter of the entire Soviet economy. Prisoners mined much of the country's nickel, gold, diamonds, coal, iron, timber and much more. They built roads, canals, and practically entire cities in some cases. So yes, being productive was very much the goal of the Gulag. Were they more productive than enterprises using free labor would have been? That is hard to say. Bureaucracy, mismanagement, poor treatment of workers, insufficient skilled labor and talent, and inadequate supply of tools and equipment limited the efficiency of the camps. But this is a different discussion.

Source: Anne Applebaum, Gulag: A History.