When you create a new character you are automatically placed in the server with the lowest population. Since Square is has added an additional 8 servers that are U.S. only people will be put into those 8 to begin with. They will not be filling up on server at a time. For example, the first 8 players to sign up will be on different servers (one on each different server).
As for being invited via a world pass, it doesn't run out. During the character creation process there is a box that says "server" that you can type in. Once you have access to a server, either the first server you started it, or any other ones that you've gained access to through world passes, you can type in that server name to be in it. Theoretically, if someone from every server gave you a world pass and you activated them all (though never created any characters on them) you could then have your pick of servers to be on by typing in the server name. If you do not have access to a server it is my understanding that the game simply ignores your entry.
Leighton