It all depends on the cut and how much is advanced.
I read a medical journal on this called "Aesthetic refinements in genioplasty: the role of the labiomental fold." And in your case since you have a overbite, possibly Class II, right angle or slightly obtuse fold angle, and your chin height is in proportion with the rest of your face then a horizonal advancement should not accentuate the tissue as much, and will male the fold slight right angle and somewhat acute. But it looks like you want some lengthening, so augmentation made need to advance and create some space in the cut, which would be filled or if the space is small enough the gap can be left and bone will ossify.
Another factor is the step that will be created. If it's substantial then Doctor may need to graft or but some type of material to lessen the step, which will push the soft tissue out further enough to give ideal fold esthetics.
You need to find a doctor, who can appreciate these factors and is not clueless about how the labiomental fold comes into play with a class II, receding, and short height chin. Implant is limited and won't do enough.
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