You will get probably a DNAS - 3xx error (something about wrong region) if you try playing a game with that setup. I got a customer who were using a euro DNAS patched game (The euro version of Winning Eleven 9) which seems to be patched to make the server think the US PS2 is a PAL PS2. And on the japanese V4 PS2 I own it gave me a DNAS - 3xx error (I don't remember the exact number) after I changed the whole NVRAM from my JP PS2 for a US one it connected and played fine. So region DOES matter even if the game is patched, it seems. I think it depends mostly on how the DNAS code got patched. A original US Disc will never boot on a unmodded JP PS2. If you boot a original US game on your JP PS2 with a mod you will probably get a DNAS - 402 error (means they saw your mod and blocked you).
About the network adapter, for that unit you need a PCMCIA network adapter card from Sony. It's used by the SCPH-10000, 15000 and 18000 models. The official hard disk for those models is external and connects to the PCMCIA card. The HDD power supply is external.
I personally think you're better getting an US PS2 even thought it's possible to make your PS2 at least useable for non DNAS online games. It should work fine if the DNAS games you intent to play are japanese tho
SCPH-10000_GH-001 SCPH-15000_GH-003 SCPH-18000_GH-008 SCPH-30001_GH-005 SCPH-30000_GH-016(V4) SCPH-30001_GH-010(V4)
2xSCPH-10190, 2xSCPH-10350, 2xSCPH-10280
"**** j0 hackers!"
-Sjeep (As seen on TOXIC OS ELF...)