Do Pokémon run away faster if you also run away?
I can only offer anecdotal evidence, but I believe that this is purely coincidental.
I got on the bus, discovered a Pokémon, and threw a ball at it, which hit. 20 minutes later, I realized that the Pokémon had jumped out of the Pokéball, but was still there for me to throw balls at.
This has happened to me twice, and it leads me to believe that the only circumstance in which a Pokémon will escape, is right after a missed throw, or right after escaping a Pokéball.