No. I always played on PvP realms, and did a fair bit of rated PvP, but didn't feel the need to kill people who were minding their own business questing unless provoked by them attacking me or ganking others. If someone substantially lower level than me attacked me, or made insulting gestures, I wouldn't flat out kill them... It was much more amusing to put a weak dot on them that would kill them if they didn't start popping CDs and let them run away.