Not discussing a theory, but fact and science. There are negatives to mowing short, but the original question was: "I'm only talking about cutting short in the fall. Does it help thicken up a lawn at all?
One big problem with LawnSite threads is that people look to pick at responses, and get away from the original question.
As long ago as the 1950s: "It is believed that frequent mowing adds to the quality of the turf. It causes the grass to stool more readily and, therefore, there is a denser population of grass leaves making up the turf. In turn, there is a greater amount of leaf surface available for the manufacture of food. If a turf is mowed less frequently, the grass has a tendency to grow taller before branching to form more leaves, and when it is cut, a relatively large portion of these leaves is removed. Only stems with relatively few leaves remain, the turf is thinned out, and is not so dense nor compact. Height of mowing is important, but if one speaks of height without taking into consideration the frequency of mowing, then his reasoning is apt to be in error because the two factors go together in the formation of a good, healthy turf." (From Michigan State: http://turf.lib.msu.edu/1950s/1955/550227.pdf
From 2002: "Mowing at the low end of the species tolerance range will stimulate shoot growth, increase tillering/shoot density, and encourage a finer leaf structure" (From Rutgers: http://www.turf.rutgers.edu/PROCEEDINGS/2002/195.pdf
) This doc also states the negatives of shorter mowing; these negatives are not that critical in fall as C3 grasses just begin their life cycle.
The original questioner asked if shorter mowing only in the fall would thicken turf, and I wanted to help him by stating from my education and experience of 20+ years that it does. My best looking lawns are now being mowed at 1.75" to 2.25" to groom them for next season. It was never my intention or dfor's intention, from his statement, to advocate consistent mowing at lower heights.