Maybe a little, but not as much as you'd think, since I deliberately caught really low level pokemon (spearow, Gastly, and Hopip all started at lv 3), and I also spent time leveling a Sentret to a Furret so I could stick it in a boxgive it to my mom.

Oh and a pidgey to like level 10 before I went back and decided I wanted Spearow instead.