Can I add sugar to the mash?

Yes, but the recipe is a bit different from what you read above. For 5 gallons of mash, try using 7 lbs. of granulated cane sugar, 5.5 lbs. of cracked corn, and 1.5 lbs. of rye. Add water to get to the 5 total gallons of volume, and stir vigorously for a couple of minutes. Put the mixture into your fermenter, and pitch the yeast. You don't need to heat this recipe until the distillation steps--the sugar is the source of fuel for the yeast. The corn and rye are really just for flavoring. This is technically called a sugar-headed corn whiskey.