Will a J-Plasma treatment help my eyes look refreshed enough to avoid a blepharoplasty? (Photo)

This will not remove excess skin and bags which is your problem. These "treatments" come and go and many people participate in the "learning curve". See an experienced blepharoplasty surgeon. The quality of the skin can be better improved after this with a phenol peel.

This is superficial ablative skin treatment.  The same level of injury is accomplished with a deep ablative fractionated laser treatment.  This treatment is getting hyped by the company that makes the device but there is no inherent advantage with the method.  It is unrealistic to expect that this treatment will accomplish something that is not currently available with other technologies.  Healing will be no faster with this treatment vs fractionated CO2.  The treatment ablated approximately 200 microns of skin.  This will actually be quite aggressive for the lower eyelid and likely to cause full thickness scaring of the eyelids.  I strongly advise you from rushing out to find this treatment.  Many of these new services have a complication curve that needs to be resolved with experience to actually produce a stable, safe treatment.  I personally think you would do better with a phenol chemical peel of the lower eyelid area.  Caveat emptor!