The yeast feeds on the flour (after it has been broken down to sugar), not on the lactose in the milk. Too much added sugar even inhibits the yeast - although there are very few bread recipes which go into that range, maybe some richer brioches and pannetones.
Sugar is added to bread for taste and texture - and I will speak generically of "sugar" here, because the differences between adding syrup, crystal sugar, honey, etc. are minimal. The taste gets obviously more sweet. The texture becomes more cakelike - the bread is moister, less elastic, with thinner crust, and easier to brown. It is also more breakable, but in a "plump" way, not in the "short" way that is characteristic of adding fats. The crumb will have smaller, more even bubbles. In total, the whole bread tastes differently with sugar than without.