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.
Thank you so much. I was looking through the complete joy of homebrewing to see how much you would use, but Papazian said nothing about priming with other "sugars" he gives corn sugar, molassas and malt, plus priming with wort.