[inquisitor]

Apple currently produces only one single version of the iPhone 3G(s) in terms of frequency bands worldwide, which supports 3G at 850, 1900, 2100 MHz. So yes, any iPhone 3G(s) - no matter where it was bought - would work on NTT DoCoMo's or Softbank's network as far as your operator has an appropriate roaming agreement or you use a local SIM.
However NTT DoCoMo also use frequency bands VI (800 MHz) and IX (1700MHz), which the iPhone may respectively doesn't support. Due to the higher range of lower frequencies NTT may rely to the 800 MHz band in rural areas, as that requires fewer cell towers and so save costs. As I recently wrote on another thread here, band VI (800 MHz) is just a subset of the American band V (850 MHz, which the iPhone supports), but unless the iPhone's firmware is ready for band VI, it might not work on band VI, allthough it's hardware would be ready for it. So depending on firmware support you might lose NTT's signal with an iPhone 3G(s) if you are in an area served by 800 or 1700 MHz basestations only.
But since Softbank sell the iPhone 3G(s) they should at least provide comprehensive coverage at 2100 MHz.
Keep in mind that the first iPhone doesn't support 3G at all and Japan has no GSM networks, but only UMTS/WCDMA, which means the classical iPhone won't work over there at all.