They do, but it's a fairly niche Adidas product. Canvas shoes are synonymous with Converse and the Converse All Star. Adidas has produced a shoe that is a copycat of the All Star (Court Vantage, shown below), and a handful of canvas boating and skateboard shoes. Adidas have traditionally produced shoes with a leather or suede upper, and lightweight running shoes that are combination of nylon and suede overlays, canvas has never been a material that Adidas has incorporated into the majority of their footwear.
Canvas is a durable lightweight woven fabric that has a range of applications: it is used in tents and rucksacks. The sportswear brands that are renowned for manufacturing canvas shoes are: Keds, Converse and Vans. These companies were founded in the United States of America. Adidas, as a German company, based in a cold climate country, probably did not view canvas a natural 'fit' for their products as it does not insulate and keep the foot as warm as leather and suede.