Does it make sense to set a constant like THEME_IMAGE_DIR?
Dark side of the moon. Definitely ;) 

Seriously though...any file that's included in every page load should be fair game to put this in. Personally I'd put it in a .module file so it's included before the theme level is even considered, but if you're only using it at the theme level then your theme's template.php file would be fine too.

As for whether or not it makes sense...if you find yourself repeating code of any kind then it makes sense to implement a constant/global/function to wrap around it. As the value in your particular case will not change in a single page load, a constant makes perfect sense to me.