The down tilt is useful for high located repeaters to reach down located stations, as mentioned in the document:
"One additional characteristic of this type of antenna is that the radiation pattern can be tilted downwards from horizontal by as much as 3 degrees by reducing the calculated half-wave element lengths 2 percent shorter. Repeaters that are located at very high elevations can take advantage of this tilted pattern to improve repeater access (down-link and up-link) by mobiles and base stations, located far down below the repeater site."
In case of ASD-B reception with collinear, it is of no use, as the maximum gain of collinear is already in horizontal direction where the farthest planes are picked.
However, for 1/2 wavelength Dipole (my Tiny Tot) it may give some advantage. See diagram below. The dark blue elliptical curve is for our 4 element Franklin, and light blue circular curve is for 1/2 wavelength Dipole.