Does a Greater sage grouse fly?

Yes

Let me explain:

The Greater Sage-Grouse is the largest grouse in North America. Males are larger than females and can grow to be 28-30 inches and weigh 6.5-8 lbs. Females grow to be 20-24 inches long and weigh half as much as males. They have brown, black and white mottled feathers that blend well with the habitat of sagebrush-steppe. Males inflate bright yellow air sacs on their necks during courtship rituals in the spring. The greater sage-grouse live primarily on sagebrush leaves, buds and flowers, and sometimes insects. They are ground nesters and typically have 5-8 chicks per brood. The chicks hatch after about 25 days and are able to fly after about 10 days.