April:
Austrailia, I believe does things different than the US and I don;t know where you are and the generator characteristics.
Your schematic wa sof a three-phase generator, which I don't THINK yours is. In any event, there is one winding that is dependent on the residua magnatism and can generate a control voltage to get thing started. Then there is a control winding, usually the rotor which is applied DC and varies the magnetic field and thus the output. Engine RPM adjusts the frequency. If the generator is capable of 12v, then that winding may be separate.
OK, that's out of the way.
In the US, our system is really called split-phase. Think of a tranformer primary being applied a high voltage such a 9 KV and the secondary being enter tapped. In a generator only supplied system the center tap gets connected to the earth and it also becomes the neutral. Neutral and Ground in a distribution system is connected together at one point. That point is the center tap of the transformer. I'm not going into detail about Grounding and bonding at this point.
The transformer would then be a 240 VAC Center tapped. What is fed to the residence is 120 V, 180 degress out of phase relative to the center TAP. The generator is likely Bifilar wound or two cables wound together and then separated for the proper phase.
So, you have a system that can deliver 240 V and 120 V. The plug would have terminals labeled L1, L2, Gnd, and Neutral.
L and N are at the same potential, Gnd should only carry fault currents.
So, there will be 120 V from G to L1 and G to L2. There will also be 240 V from L1 to L2. So, nothing is in parallel. The currents are such that Neutral carries the unbalanced current between L1 and H and L2 and G. So, if L1 carries 10 A and L2 carries 10 A, the neutral carries 0 amps.
If L1 carries 15A and L2 carries 10 A, then 5 A is carried by the neutral. The neutral current can be in either direction in the wire.
OK, here is where the fun starts. Some welders are designed to work on single or 3 phase and you might say What?
Internally, the welder looks like a transformer with 3 primaries wound on the same core. In this case, you could, in theory, supply 2 of the phases. and increase the output. You don't need three.
You can't exceed the design of the input currents though. And the cool part, phase doesn;t matter and so what, if one of the phases is disconnected.
It may depend on internal circuitry on what's allowed but the three phases can be phase angle fired together or independently, but only one is used for the reference. The unconnected phase will still see a voltage on it, but with no current.
I think some of these concepts is what's confusing everybody.
So, if the welder is single or three phase, then operating it on two separate unsynced single phase sources should be permissible.
Does any of this help? There are pieces missing and there are lots of things going on and some won't make sense to some. The reason why I know is that I worked on a three phase 208 VAC 15 KVDC 1 Amp power supply that effectively created DC. Three phase really wasn;t necessary, but it's a good clean way of the high power it needed. The box required 208 50 Amp 3 phase. Another similar unit required 70 A 3-phase 208. taps were available for the transformer.
So, by understanding the system, and in this specific case it's possible that 1 to 3 INDEPENDENT AC sources of the same amplitude and various phases would effectively increase the power output available from the welder. One phase can also be totally left out.
The AC sources add to the available current to the magnetics. This only works if the transformer used has multiple INDEPENDENT or "Y-connected" primaries and a single secondary.
Sorry April, I was thinking the TYPICAL combining of outputs. This isn't typical and would throw probably 98-99% of the people here off.