You might have a few issues, but to be fair the world is usually open during the quieter hours, so I shouldn't see why you shouldn't be able to get a transfer. I believe it's only closed due to how busy our server is, being one of the busiest in the game.
It's usually open for creation at around midnight for the UK, and then a good while through the early hours of the morning, this is going by the same time as the server time. I'm not sure how the transfer service works, but they might wait until these quieter hours to actually transfer your character over, while the server isn't congested.