Unless the path to the ground of the device, and then from there to actual ground, is shorter, then nothing will flow that way.

That's not true. Electricity will take all available paths to return to ground, with current flow relative to the resistance present. In other words, two low resistance paths will share similar amounts of current when both are connected to power.

If you were touching anything connected to that 'ground' wire while also connected to a true ground yourself; you could receive a harmful shock from plugging this in, even with a breaker in-line and successfully tripping. A GFCI device should prevent that shock, but a regular breaker will not trip fast enough.