Will the chin implant stretch my "double chin" enough to not need Liposuction? (photos)

That hanging hammock in your underchin is due to the short pull of the mandibular symphisis (chin); with an implant this pull will not increase.To obtain that and because of many other advantages I recommend you go for sliding genioplasty.Being an option, chin implants have serious disadvantages, specially in
the mid and long term, patients are rarely happy with them after 5-6
years, all are out by then or later.Consider the chin advancement by means of sliding genioplasty, the advantages are:-lifetime procedure, no more revision or renewal procedures-more natural than implants-no visibility of implant edges during gestures-improves
the double chin effect at the sub-mental muscles (floor of mouth)
hammock caused by lack of tension there; also improves the shape and
tension of perioral muscles; implants do no offer this feature-horse-shoe enhancement, covering the chin and also the jaw sides of it-no future displacements or neuritis of mental nerves-practically zero infections and 100% healing of bones-no
need for complex plates and screws that may need future removal; just
steel wires synthesis may suffice, they stay buried into bone callusThe cons are:-expensive, but cheap if you consider the lifetime pros-technically
demanding, few surgeons are experienced or comfortable (though I
personally perform 100% of the chin augmentations by this osseous
method, always after offering the patients both options)-scary for the patient (though not so much if you explain well the stuff around it)

I'm also on the fence for whether or not you should get liposuction. I'm inclined towards just chin augmentation. You can alway go back and take more out. It's very difficult to put back fat in though. Your face also looks thin and I'm not sure that's not actual fat tissue there. Good luck! 

A chin implant will not stretch your neck tissues out, only a sliding genioplasty will change the neck as well as the chin. If you choose an implant then you should have liposuction.