As long as they affix sufficient postage, it's 100% as far as I know. The postal system in Japan is at least as efficient as the one in the US. I've never had problems mailing in either direction.
Exception: a gift package sent by my mother did get bounced at customs once for some reason that was never made clear (maybe because it had food in it). That wouldn't happen to letters, though.
For me in Japan, I have recently been having troubles. I have had a few letters and packages taking a month or never coming. I think the reason has to do with some portion of world mail for some reason is being sorted in Denmark and they are messing up. The alternative is that I have been marked by the CIA and they want to check whether it really is the English edition of the incredibles from my mom or a BOMB from osama. :
(I know I am going to get a visit from some men in dark suits for this post)
We us a Great mail service in Green Cove springs Florida. Ultra Reliable, Very Responsive and Very reasonable. They also helped with Florida Domicile. Not only that the DMV knows about them and got us Florida Drivers Licenses so easily.