Yes. I actually happened to go check on the status (using the link in the reservation email from last night) and it was ready to be completed, and I had not received the second email yet. I checked out with no issues, was able to keep my unlimited data (AT&T), and the shipping estimate is still the same as when I reserved it last night (7-10 days, iPhone 6+ 128GB).
I was going to do the same with my wife's order, but then she actually got the second email right when I was about to go check on it anyway. No issues with her order either, and it was confirmed for delivery on the 19th (iPhone 6 64GB). Also AT&T.
So even if you haven't received the second email, keep checking that status link.