I doubt it makes much difference if any in the longevity of the strings. Things wear out and break down with use and time, and that of course includes twine used for shades.
I have a motorhome and generally drive with them up because I like to be able to see out the windows when driving; it's occasionally helpful for maneuvering in tight corners and such. I do have one that tends to work its way down with vibration and bounces, so even though it starts in the up position it's usually at least partly down when I arrive. Such is life.
