Probably during the week. People can't take off of work forever, every human needs to sleep eventually, and I'm sure a lot of the EU players still kicking around the NA servers will start taking those free transfers.
A lot of the people who are sitting there for 5, 10, even 20+ hours nonstop clicking on Raubahn, no matter how much they may not want to, will have to go back to the real world in a day or two.
Then everyone will start getting back to their normal schedules instead of living at the PC all weekend being disappointed.
On top of that a new raid launches Tuesday in World of Warcraft, so I'd imagine a lot of the WoW players with more loyalty to WoW than FFXIV will just say screw it and go do that instead.