I won't post any pictures, because it's something you need to see in the game for yourself to really believe.
[url]http://www.reddit.com/r/DestinyTheGame/comments/2i8mqv/the_traveler_does_seem_to_be_healing_but_only_in/[/url]
After reading this post on reddit, I decided I'd see for myself it this was real. I waiting a full day/night cycle, and as the sun came up and the day went by, the Traveler [b]was definetly more healed[/b]. As I said, this is something you have to see for yourself to believe. Next time you're at the tower during the day, look at the Traveler, especially the bottom right part (from the Tower's perspective), and see for yourself.