Of course not. Sakura and Hinata may both love Naruto, but there not that immature. Maybe if it was Ino Sakura would fight:). Hinata would never fight over Naruto. She's too nice and shy to ever do that.
Sasuka and Naruto have their final fight at the end of the Naruto manga. Their final attack destroys their dominant hands, and as they lay together with their blood intermingling, Sasuke admits defeat.