Is a deep mentolabial sulcus an aesthetic concern when wanting to increase horizontal chin fullness with implant? (Photo)

I am impressed with the detailed nature of your question.  You are correct that you have both a deep labiomental sulcus and a weak chin.  In this situation, I do not believe a chin implant is contraindicated.  I would be conservative with your chin implant, and I would not place an over large implant.  A large chin implant will make the crease appear to deep but a small or medium chin implant would help with your result of a neck lift.  I hope this helps  

If you have a chin augmentation that increases both horizontal and vertical chin projection (which you need), your deeper labiomental sulcus will not be a concern. But if you increase horizontal projection of the chin only, the labiomental fold will get deeper.

The photograph demonstrates significant fatty deposits in the neck, and a mildly weak  chin profile. A neck lift with a small chin implant can help  give a better jawline definition without having to worry about in mental labial sulcus.  For many examples, please see the video and the link below