You sure can, but you need to calculate the amounts differently. Brown sugar is composed of Sucrose + molasses. Sucrose is a disaccharide of Glucose and Fructose. Typically, you prime with D-Glucose (dextrose, corn sugar, etc) only, so you get a little more "bang for your buck" for each molecule of sucrose.
That said, for 2.5vol CO2, you'll prime with 0.82oz/gal Sucrose or 0.95oz/gal dextrose.