Yes. Here's a higher end "grocery store shelf" bread maker:

http://www.pepperidgefarm.com/FreshBreadsGateway.aspx

2 to 4 grams of sugar per slice is typical there. That sort of bread is prepared at large regional bakeries.

Decent grocers will also have a fresh bakery, with somewhat more variety to the product, and probably breads with little added sugar.

If you live in a decent size town, there will also be one or more store front bakeries that uses a shorter list of ingredients (I almost said they are more traditional, but I'm sure they are mostly using big mixers and nice ovens and the like).

Yeasts are perfectly capable of splitting starches, you don't need any sugar.