There is no official word yet, but reports from those who have played E3 and post-E3 builds of the multiplayer game indicate that the health bar in the HUD, and even the idea of "health" has been removed from Halo 2 entirely, and replaced with a stronger, faster-regenerating shield.
Editor's Note: For the multiplayer game, I think this is a real plus. When you go up against a player in this system, you can get visual feedback on how close you are to a kill based on the appearance of the shield, if the system works as it does in Halo 1. If you get the shields down completely now, you should be getting a kill. If you don't, the player's shield will quickly regenerate and he'll be a hard target again. In Halo 1 multiplayer, someone could be running around with full shields but almost no health and wouldn't necessarily be an easy target, but would be an easier target-- with no way to visually differentiate him from other players. In short, I always felt cheated by health in the single player game-- it felt like a powerup.
Now, the single player is another story, and the Game Informer article seems to indicate that this change was inspired not by the multiplayer game, but by the single player campaign, where having low health at a checkpoint with no medkits available nearby could make it nearly impossible to advance. Although I can understand that perspective, for me this takes away from a legitimate source of dramatic tension in the game. There's nothing more rewarding than getting through a tough part of the game that you had to start with low health. In fact, in some cases I've intentionally avoided medkits until a confrontation is over in order to make the encounter seem more interesting.