IMO, produces energy is a poor way of describing at this. They produce ~1,000 parts light:99,001 parts heat per 100,000 units of electricity and 1 units of fusion. In other words 100,000 units of electricity liberates 1 unit of fusion power.
Isn't that like saying a lightbulb doesn't use any energy because its output of heat and light equals the energy input? Or that I didn't use any money shopping because the cash all stayed in the economy?
Sure, a light-bulb does not destroy any energy, it uses electricity and increases Entropy. If you want to say it consumes something then a light bulb consumes the potential to create Order by transforming electricity into heat and light.
It sounds like the argument is considering what the output energy might be used for. If you want a fusion device to power your heating and lighting, then the "waste" heat and light from the device may actually be useful.
It's like replacing the radiators in your house with servers or bitcoin miners; you still pay for electricity, and it's still warming up your house, but you get compute cycles or bitcoins "for free". If the waste heat/light of a fusion device is of comparable efficiency as conventional heaters/lighting, then we're "breaking even"; if the device manages to perform any fusion, that liberated energy would be a "net positive".
Of course, a fusor doesn't seem like a particularly good idea for household heating or lighting, and that argument is completely inapplicable to things like power plants.
I looked at building one a couple of years ago before deciding I couldn't afford the equipment to make sure it was safe, but I always had this in the back of my mind: Don't all nuclear reactors use heat as the main output? To drive steam generators (like a conventional plant) or solid-state devices like a peltier-based battery used in satellites?
If you put a bounding box around a Farnsworth Fusor, and put in 100W of energy, would you not get a little more than 100W output from the fusion reaction?
Obviously still not viable as self-sustaining, since 100W of electric energy in would be lower entropy than the 100W+ coming out, but it would be a method of producing some energy as long as it's fed from another source.
Obviously, using a heat pump would be a much better way of turning 100W of electricity in to >100W heat, but still, a Fusor isn't net energy negative (although it is terrible with conversion of entropy).
You are ignoring the energy in the fuel. Which is arguably a reasonable thing to do as we don't have great fusion reactors yet and H Bombs are not exactly sold at Home Depot. But, it's still the kind of fuzzy thinking that leads you to assuming bad ideas will work.
As to 100W vs. > 100W. 100.001W might as well just be 100W in just about any meaningful way. However, Jet is vastly cheaper per watt of liberated fusion energy. https://en.wikipedia.org/wiki/Joint_European_Torus
It depends what the main power output is. Neutrons from D-D or D-T (deuterium-tritium) are really hard to convert into electricity, but some types of fusion like p-B11 (hydrogen/boron) generates alpha particles that can be directly converted to electricity.
https://en.wikipedia.org/wiki/Fusion_energy_gain_factor is meaningful, but it's talking about inputs not outputs.
PS: Ok, heat is a poor description. 1,000 pars light, 99,000.9 units of heat, and 0.1 unit high energy particle radiation.