It took over a week before my debit card arrived. And then they ended up canceling my account anyway due to a "mail drop" address. I wrote up my whole story on my blog.

tl;dr
- Opening a Citi checking account online with a private mailbox will get your account canceled
- Opening a Citi credit card online with a private mailbox is okay
- You may be able to open a Citi checking account in branch with a private mailbox (haven't tested yet)