How though?

By using Social Security Numbers? What about the Canadian members? They don't have SSNs.

Who'd be responsible for the maintenance of this database? I'm thinking that it be a lot of work compiling the info, updating the info with new members, deleting deceased members, etc. etc.

That's just too much work.

I don't know why an already initiated member, after learning about the sanctity of ritual, would even want to initiate into another NPC. I wouldn't know how often this takes place, but I think it's safe to say that it doesn't happen often enough to merit creating a Panhellenic database.