Just run collision with whatever mesh happens to be the current LOD version. This will cause errors under a few unlikely conditions, and the potential for error is negligible.
LOD will also improve rendering performance significantly, if you are drawing a demanding scene. If you can reduce your render polycount by 50%, then a transform-rate limited scene will draw faster.
If you're just moving a few objects around on the screen, LOD is unlikely to make any real difference, since these scenes are fill-rate limited. A far away object does not increase the fil-rate demand hardly at all, but it will increase the transform-rate demand, by a lot. Until you get to the point where you have enough polys to actually slow down the renderer transformations, LOD won't make any difference.
LOD will also improve rendering performance significantly, if you are drawing a demanding scene. If you can reduce your render polycount by 50%, then a transform-rate limited scene will draw faster.
If you're just moving a few objects around on the screen, LOD is unlikely to make any real difference, since these scenes are fill-rate limited. A far away object does not increase the fil-rate demand hardly at all, but it will increase the transform-rate demand, by a lot. Until you get to the point where you have enough polys to actually slow down the renderer transformations, LOD won't make any difference.