You can, but you will have completely different results. Brown sugar has molasses added to it, which gives the sugar more flavor, but also makes the cookies much more tender and moist. Brown sugar will attract and absorb the liquid in the dough, so that is why the cookies will be significantly more tender than if you use granulated sugar. Molasses is acidic, so it will react with the baking soda, which is important too. Raw cane sugar is not the same thing as brown sugar. It doesn't have any molasses added to it. Also, raw cane sugar dissolves a lot harder than granulated sugar, so in addition to the cookie bars being more dry and hard, the sugar may not melt completely when you make the batter. As the bars bake, the granules of sugar will melt and you'll have tiny dots all throughout your cookies.