One might answer that with, what exactly is natural pitch? I mention this as equal temprement is our best attempt at defining what pitch should be, and is an approximation in many areas, varies with key and scale and so on. Have a look at a couple of products by companies such as TCElectronics
http://www.tc-helicon.com/VoiceLive . Corrects pitch and creates harmonies, goes into quite a bit of discussion on what is pitch.
Regarding tonal languages having better pitch recognition, I think the answer may be yes and no. Yes perhaps because pitch variations are much more closely watched , and no, because the tonal changes in no way relate to pitches that we are familiar with , such as those defined by equal temperament. The pitch changes in an oriental language (although vary from country to county) are things like constant pitch, rising pitch, dropped and dipped and so on.
An interesting note, is that in the far east is still a large number of instruments that do not conform to equal temperament , giving the western listener the impression it is out of tune. A great number of Chinese instruments are like this and an instrument played a Thai boxing also has this phenomena.