Yes. A client did ask this very question the other day, albeit, with humor in her voice. We laughed. The question made me pause. As a hairstylist I am asked many things, or am considered many things, some of which are spoken and not spoken. Sometimes I am seen as a magician, who performs daring acts of color combinations, or haircuts that make one take a second look. No, I don't pull rabbits out of hats, and I don't disappear in front of the mirror, or make lines disappear on the face. But yes, I can make someone look thinner with a haircut. It's all about shape of the head, and of the haircut. Whattype of hair, the texture, the condition, and the clients willingness to let go of the concept "more hair is better", are all elements to consider before I cut. Different line designs accent different features, or facial shapes, or they can completely drag them down.
In general, when someone has a broad, square shape face, I am going to go in and soften the face by cutting a nice, layered hair cut, how short the layers are depend on, again, how much hair a person has, or texture. I am not talking about bulky, fat layers, but square layers, more shaped around the face. The length can be mid length, or shorter, again depending on hair type and texture. If shorter length is desired, I would go in and do round layers quite short, leave some hair in front of the ear, but shorter above the ear, leaving some hair on the neck. In front, I tend to cut asymmetrically. It works to offset a long, and or broad face.
If a client has a round face, I would tend to want to elongate their look, and take hair away from thier face, by creating a oval shape in the perimeter. Then graduate into round layers, and a bit more movement Again, this is very general.
If a client has a heart shaped face, I would tend to do bobs, shorter, more dramatic looks, unless they prefer length, too long is too much of a drag on the face, but some women want it anyway.
Although, I don't do face lifts, or weight reduction, a great haircut can make a dramatic change in someone looking more alive, taller, more chic, and definitely thinner.