Depends a) how many e-mails they're sending and b) how good their e-mailer is.
My company has a crappy e-mailer system and to send out five thousand e-mails takes about an hour and a half. S-E is used to handling much larger quantities on their group e-mails, so I presume they have a much awesomer system than that.
I think it would have arrived by now, if it were going to. :(
