The unique ID is from the transponder -- not it's "data" that is displayed. Since most GPS units on AIS units are pretty "plain Jane" you would warble around, even at rest. While you might get a less superimposed image at rest (though I'm not sure), if you were moving, I suspect that you'd get a distorted text or two super-imposed images.
I'm not sure that using two AIS units on one vessell is allowed by regulation.