Since HeartGold is remake of the original Gold, just like FireRed was a remake of the original Red, yes you could find Entei again, although it would be incredibly difficult. Just make sure to train a Ghost type pokemon to use Mean Look to make sure that he can't run away because Entei, Suicune and Raikou will all run away once its their turn.
But all three know Roar, which can scare away your pokémon ignoring the status effect of Mean Look
If you have already caught Entei, you cannot catch a second legit Entei on the same file.
However, if you accidentally killed it, then you have to fight the Elite Four in order for it to respawn.