Earth ground has no mystical magical qualities with respect to electricity, particularly not to electricity which is transformer isolated from the mains. Current flow requires a completed circuit *from* the source, *through* the load, and *back* to the source. Earth ground is not involved. An Earth ground doesn't "soak up" electricity. It is simply a large sheet conductance which *may* serve as an alternative conductor for electrical current back to the service entrance connection under certain *fault* conditions (for example a short between the primary and secondary windings of the welding transformer).
To illustrate this, once you have your welder hooked up, try to strike an arc to Earth (dirt, concrete floor, etc). Nothing will happen. There isn't a complete circuit, and no current will flow. Now try to strike an arc to some metallic piece which has the welder return clamp attached to it. Boy howdy, now you get some action.
As the old electrician used to say, "It takes two wires to make a light."
Gary