The AbBelts are general TENS units (Transcutaneous Electrical Nerve Stimulation). They do stimulate the superficial muscle directly under the skin, but not very much. They do not burn fat at all in any way shape of form.
They are illegally sold if without a prescription, because, although I really do not think they are dangerous (I do have some knowledge in this field), they are used for pain relief of chronic and acute muscle injury.
Simply, TENS effects only the superficial nerves beneath the skin, which helps the body to produce endorphins. A TENS unit shock will also the make the muscle contract so that you do not get muscle atrophy (wasting). But the contraction is nothing like a crunch, it is a very minor contraction simply to help keep the muscle healthy while you heal. Also, after you use one (they are generally prescriped in 15 minute intervals for no more than about an hour) you may feel sore, as if you worked out, but you will not have any real benefits of working out such as elevated heart rate and the stresing and building of gross/core muscle.
A TENS unit does not cure the underlying cause of pain if you have a real injury like a pulled muscle, just makes the pain so you don't feel it.
So it would seem that unless your abs are so woefully out of shape that you couldn't even tighten your abs, an AbBelt might be helpful, but methinks it probably won't help you at all.