Can a lower bleph with eye fat repositioning cause a sunken appearance?

A surgeon suggested that I get fat repositioning for my lower eyes, despite not having puffy eye bags (I only have hollowness in the tear trough) - My concern is that removing the little bit of fat that I have directly under my eye will make that area appear sunken. When the fat pad is moved from the area directly under the lid for filling tear troughs, will it possibly cause a deficiency in the area it was removed from?