Yes, they can. The question is should you do it. Yeasts prefer different sugars over others and the majority of sugar you want your yeast to consume are maltose sugars. By creating a starter with a different food source other than maltose, the yeast can stress a bit as they have to change gears and switch over to a different food source.
Stress in yeast produces off flavors that usually express themselves in fruity esters or spicy phelonics, or both. Depending on the style of the beer, this is either a good thing or a bad thing. For example, it'd make no difference in a nice Belgian ale as fruit and spice is a desirable characteristic of the style of beer. However, if you're brewing a pilsner, these flavors would be considered flaws and would be unwanted.