No, you can not battle/capture Latios/Latias in any of the Hoenn versions of the game without beating the Elite Four+the Pokemon Champion. Beating the Elite Four triggers an event in Emerald at the player's house in which you can decide whether Latios or Latias appears in your game. To do this, go to your house after beating the Pokemon Champion, and you will see your mother at the television. She asks the player what color "that Pokemon" was, and you can choose from either Blue or Red. The Player's answer decides which one appears in your game. After that, the encounters are at random in areas determined by a game-specific, randomly-generated pattern.