Pierce sausages; cut each diagonally into 1-inch pieces. Heat the oil in a large nonstick skillet over medium-high heat. Add the sausage; cook 3 minutes or until browned. Add the wine and mushrooms; cover, reduce heat, and cook 10 minutes. Stir occasionally. Remove sausage from pan. Cook the mushroom mixture over medium-high heat 5 minutes or until liquid almost evaporates. Stir in the basil and tomatoes; cook 1 minute or until heated. Return sausage to pan; keep warm.
While sauce is simmering, prepare polenta. Bring water to a boil in a medium saucepan; stir in polenta, garlic powder, sugar, and salt. Reduce heat to low; cook until thick (about 5 minutes), stirring frequently. Stir in cheese. Serve with sausage mixture.