My main concern is how the increased fat in the bloodstream would affect the health of the patient. While I don't have the scientific background of some people here, it does seem to me that if a hormone is added to the blood that stimulates the release of fat, the body rest of the body wouldn't be prepared -- I assume that when actions like that are taken naturally, there are some changes in the blood vessels and tissue the nutrient is being directed to. I would think it would cause increased risk of strokes and other afflictions related to clogged blood vessels, so the machine would have to be operated in very small increments. Assuming that this is taking place in a medical setting, as mentioned before, I would expect it to be nearly as much of a time waster as going to the gym, without even the other health benefits of working out. It also would cost more for the patients, given how they'd have a doctor charging them for the time spent have fat removed.
Well you might not need the doctor or the medical setting if you were impanted with an artificial cardiac pacemaker and a cardioverter-defibrillator. Those would moniter heart rate and correct any inconsistencies, and restart the heart if it stopped.
Yes the excess fat would clog your blood stream. However HDL Cholesterol and other things like serum albumin could, if injected in similiarly massive quanities to the epinephrine and norepinephrine, transport fatty acids and LDL cholesterol to the liver, as well as help clean out your blood vessels in the case of HDL choleserol. When the Liver recieves the fatty acids and LDL cholesterol, it will send it to the gall bladder in the form of bile for use in Enterohepatic circulation (fat digestion and digestion of other things). You could have the machine hooked up to the veins carrying these to and from the gall bladder, and have that blood sucked into the machine where the fats are removed, while blood reserves are pumped back into the veins. It goes to teh gall bladder first because that is where your body concentrates bile before sending it to the small intestine.
You would have to provide the body with the nutreints to manfufacture the bile, and continous nutreint injection to make up fro amount of nutrients lost inteh production of the bile. If there are hormones that stimulate bile production, those would also be needed.
This would all be famouslly expensive, but you could do it while watching TV or posting on a forum. As long as the machine is sophisticated enough that is, some other machines might require doctor supervision.