Would Liposuction Help Nasolabial Folds and Under Jowling?

Very good question. Sometimes if the patient doesn't want a cheek or face lift I have removed part of the "mountain " and filled the "valley". This will help more than just the filler, but not as much as lifting the tissue.

A more accepted theory as to the development of deeper smile or nasolabial or meilolabial folds is that there is not an abundance of fat to the side of the fold, but atrophy or loss of fat in the medial (inner) and mid cheek. This loss of fat creates a loss of support and the cheek falls folding over and making a deeper smile crease. Volumization of the cheek areas that have lost fat may help lift the cheek and lessen the fold. Attempts at liposuction of the "meaty" cheek next to the smile fold have been attempted but are not universally accepted as a good treatment for this condition.

Conservative liposuction of the tissue that's causing your nasolabial folds has been described. Specifically, Tonnard and Verpaele from Belgium described this technique as part of a MACS-Lift, short scar facelift in patients with very heavy folds.
You should discuss this with your surgeon. I think this must be done carefully since indentations or asymmetery in the midfacial area could result.
I hope you find this helpful.