Until now my point of view has been that the Pandaren are influenced, at least to some degree, by the Dreamworks movie. But now I am not so sure. MMO-Champion has links to a topic where a blue posted this:
This is something I want to touch on a bit more. People seem to think that Pandaren were a joke, a throw away easter egg that we never fully intended as a playable race.

I will direct you to recall the Warcraft RPG (pen and paper) manuals released in 2003. While much of it hasn't been canon for quite some time, the Pandaren occupy a greater amount of pages and space within the manuals to establish their lore and story than pretty much every other creature on Azeroth. To give it some context, they occupy the same number of pages as Trolls in the Monster Manual, and share the same amount space in the Alliance and Horde Compendium with Orcs or Humans, and just like them ... you guessed it... Pandaren were a playable race.

[...]

It would simply be inaccurate to state that Pandaren were a throw away. Our intent, going back to Warcraft III, when the vast majority of the world lore and story was established for the franchise, was always to have a deep and rich history for a race known as the Pandaren.
And then someone linked to this 2003 drawing by Chris Metzen. The Pandaren in that drawing looks a heck of a lot like the main character in the movie... except that the drawing pre-dates the film by about five years.