Does herobrine exist on minecraft xbox 360 edition or indeed any platform of minecraft?

Nope. He does not exist on any platform in Minecraft, It's just a creepy character made up by the community.

He never has and is unlikely to ever exist in any form, on any device.

The only way Herobrine will ever be implemented into a Minecraft game is if someone creates a PC mod that codes for a Herobrine-esque NPC which might stalk you, or do other annoying things in your world.