Nope, the PvP server is really a FactionvFaction server. There are certain circumstances where another person in your faction can attack you:
1) You accept their challenge to a duel
2) Your honor is so low, due to you being an all-around scumbag, that you are Kill On Sight to everyone
Otherwise, they're the Horde! They're your buddies! They wouldn't go randomly attacking their allies, right? No, you ARE kill-on-sight to every two-bit Alliance character...