polenta uses a medium to course grind, while cornbread uses a fine grind as well as wheat flour to keep it light.

that said & assuming a trip to the grocer is out of the question... soaking the polenta in milk or water should soften it up enough prior to baking to keep the cornbread from being gritty. or use a food processor to grind it a bit further... if you can grind coffee or spices, how is grain any different?

what is more critical is the proportions of corn & wheat flour to liquid to get a smooth flavorful mixture that is not too dense when baked... the best tasting cornbread I ever had was made by a southerner who used bacon grease for the lipid of choice.