Is it possible to lose subplatysmal fat through weight loss?

If someone is overweight, I would say that it is possible to lose subplatysmal fat with weight loss.  I would recommend getting to an appropriate weight for your height and then re-evaluating the appearance under your chin.  

It's important to be at your ideal body weight with a BMI of less than 34 and then have the diet resistant fat removed. A necklift procedure is required to remove fatty deposits underneath the  Platysma muscle, and then a platysma-plasty is required. No skin removal is required on patients less than 50 years of age. Both of these maneuvers will significantly improve the jawline.   Liposuction can only remove the fatty deposits above the platysma muscle. For more information and many examples of neck lift procedures,  please see the link and the video below

I'll fat cells in your body will shrink with weight loss.
To get the desired facial contour with weight loss alone may be a stretch.
I generally don't refer to the names of other doctors when posting on real self however I believe Dr. Palmer has stated in answer to your question very well.
Consider a second opinion through an in person consultation
Best,
Mats Hagstrom M.D.

 Hi, non smiling photos of your face from the front and side would help in the evaluation.  I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  If the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  If the chin is weak and there is excess fat below the chin (most often it's subcutaneous fat) it can be reduced with liposuction.  Most of the submittal fat is above the platysma muscle and is easy to access.  If you want to loose some weight to see if it gives you the look that you desire, there's no harm in that at a all.  The issue with losing fat from the face is that the amount of facial fat is typically a very small percentage of the body's total fat which means losing weight will have a nominal effect on any specific area of the face, including the area below your chin...unless you lost a large amount of weight.
 Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty.  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone. Hope this helps.