Gravity works in 3D, not only when you just happen to pass through a certain line. And the speed with which we pass through that line is much too slow to have such a definite deadline. Plus, as you say, even if there were some results, the effects would be spread over a very long period.
American Scientist says:
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The sun oscillates through the plane of the galaxy with an amplitude of about 230 light-years, crossing the plane every 33 million years.
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With such a slow movement (once every 33 million years), and with the thickness of the Milky Way, there would be no noticeable difference between this year and seven years later in gravitational pull of other stars. All this supposing that we are anywhere near a crossing of the galactic plane, of which I find no notice.
Furthermore, from the same article:
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A plot of the sun's course through our galactic locale shows that the sun has been traveling through the Gould's Belt interior in a region of very low average interstellar density for several million years. The sun is unlikely to have encountered a large, dense interstellar cloud in this relatively benign region during this time. Although our solar system is in the process of emerging from the Local Bubble, the sun's trajectory suggests that it will probably not encounter a large, dense cloud for at least several more million years.
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So not much stuff is nearby, meaning again less chance of interstellar disasters and so on.
According to
this 11 page pdf, the last crossing of the galactic plane is +- 1,5 million years ago, and the next influx of large comets (related to it) +- 1 million years away. So the 2012 date is pure nonsense as related to the crossing of the galactic plane.