Surprise: it doe's not!
With two characters, one with agility 10 and other with agility 1 I run from Goodsprings to Primm using same route and same dress. It took approximately 3min 30sec of real time in both cases. Difference been just few seconds, easily attributed to rendering and small deviation in course.
If you are not using VATS, agility is useless unless you want some perks.
