Exercising, at the least to the extent that most people can manage it, is an incredibly inefficient way to burn fat. You need to dedicate large blocks of times regularly to make a significant impact (which is why changing your eating habits is a much more valuable way to control weight). And being overweight often makes exercise difficult in and of itself, and far less enjoyable. Some, like myself, exercise as much as possible (probably 3-4 hours a week of moderate exercise, and 4-8 hours of light exercise like extended walks), and still find themselves overweight simply because they have difficulty controlling their diet (and I'll be honest, the medication has been making that worse)
There are a lot of complex chemical reactions taking place when you burn adipose tissue in your body. Making a machine/process to do it is plausible, but I can't see it being done without lots of incisions to actually reach fat tissues.
I don't see why the machine would have to do it directly to the given cells, since our body manages to use fat energy from pretty much everywhere for pretty much everything, no?
The thing is, exercise is the
only way your body is triggered to access its fat stores, and produce energy from it; stored adipose is only broken down in muscle tissues when they are overworked, or there's no stored glycogen (short-term energy storage) available.
Hypothetically, you could isolate the hormone that forced fat-storing cells to dump fat molecules into the bloodstream, administer that to people, and then filter it from the blood dialysis-style, but unnaturally high amounts of fat in the bloodstream wrecks havoc on your blood vessels, causing them to harden... and I'm not sure if there is such a hormone, nor if it strictly affects the body's fat stores. Again, exercise is the only way I know of that the body can trigger that mechanism in a safe way.
Problem is, would the harvesting cost more than the energy produced? That is the obstacle we need to overcome, and depending on how the machine works... maybe!
Though really it probably wouldn't even be able to power itself unless the designers were really smart about it...
We've been trying to design engines that could be powered by calories for years. Though I can't find the source now, I did read about a working model a number of years ago, though it required a lot of chemical treatments to break food items (I think it was strictly plants) down into combustible chemicals, and was still pretty inefficient. With the exception of solar cells, we don't yet have the equipment or tech needed to generate electricity on a chemical level... we're still doing it physically through properties of electromagnetism, generally with some kind of fuel heating water to spin a turbine... or using something like wind or water flow to spin the turbine.