Both ELCI and GFCI detect ground faults but with different trip points. With either one, you do not need the green wire to be connected to the socket for the circuit to trip.
BUT.. the hot and neutral must still be referenced to ground somewhere. Even if the green wire is not present, the nuetral and earth ground will normally be connected back at the fuse box and this establishes the reference to ground.
Say you are in a marina with shore power that is referenced to ground at the marina fuse box. If you measure voltage to ground (and the water will be at ground), you will see zero volts on neutral and 110V on black. If the black wire were to touch the water, current would flow because there is a 110V potential between the black and water. That is a ground fault because that current did not return on the white wire and ELCI or GFCI would trip. Put both black and white in the water. Black has 110VAC to the water, White has near 0 VAC to the water. Lots more current flows from the black to the water than from the white. Ground fault again.. ELCI or GFCI would trip.
But now lets say we have a truly isolated power source with just black and white such as you might have with a genset comletely missing the ground (or it is truly floating). If you were to put just the hot black wire in the water, there is no ground path or return circuit. No current would flow. It would be like putting your tongue on only one terminal of a 9 volt battery. Nothing happens. You have to touch both terminals to get current flow. If you put both black and white wires in the water of this completely floating power source, you would measure something similar to the 62 volts mentioned earlier. You would see 62 volts from hot to the water and 62 volts from the white to the water. Current would be flowing between the hot and neutral through the water but it would be balanced and equal. All the current flowing would be between the black and white wires like normally happens with a load. So no ELCI/ GFCI trip.
I have not looked at those generators to tell if the ground is actually completely floating from hot and neutral. There may be some trick that the generator uses for that ground (like capacities coupling which could trip GFCI with a transient fault) but if the hot and neutral are truly completely isolated from hot and ground, I dont see how either ELCI or GFCI could trip.