About this question, I am afraid that I don't have enough knowledge to answer you since I have never used a "non-original" FFXI DVD to try. However, for sure that you need a set of serial numbers which comes with original FFXI DVD for registration.
There is another question to your situation: where is your PS2 from? Europe? Because PS2 HDD unit currently only works on Japanese PS2, without PS2 HDD working, you will not be able to play FFXI either...
The best solution will be: Buy Japanese version of PS2, PS2 HDD, and FFXI disc set with comes with a set of serial numbers.
If you still have any further question, please don't hesitate to ask! ^^