The cut you are describing is an (isolated) osteotomy to the mandibular border. It is commonly referred to as a 'chin wing'. So your question 'translates' to asking how common it is for doctors who do genioplasties to also perform chin wings. I don't know the answer. But I do know that it's very common for doctors who do 'chin wings' to extend their cuts to the back molars.
Thanks for the answer kavan.Just to clarify: Sometimes they extend their cuts "just" to the back molars but not all the way back to the angle of the mandible? I would assume that in such a case it would most likely make sense to move the bone just forward along the mandibular plane.
The cut for the chinwing is all the way back to the angle of the mandible which is what I thought was meant when you said 'back to the molars' as in PAST the molars.