Yes, they can! To get started, turn all of your burners to high and close your cover for about 15 minutes to heat the grill. When you’re ready to start cooking, leave your main burner on high and turn off all of your other burners. Grill temperature should ideally be between 325 and 350 degrees. Brush clean and oil your cooking grates. Then place your drumsticks, skin side down, on the side of your barbecue that is turned off. You will be cooking your chicken on this side only. Close your lid and cook for 25 minutes. Rotate the chicken drumsticks from the cooler side of the barbecue to the side closest to the hot part of the grill. Cover and cook until drumsticks register 185 to 190 degrees, another 20 to 30 minutes, depending on the size of your drumsticks. Once cooked, move all of your drumsticks to the hot side of your grill and cook, turning occasionally, until the skin is nicely charred, about 5 more minutes. Transfer chicken to serving platter and brush with sauce.