Looks like 4:30 pm EST was the cutoff time.
http://www.engadget.com/2010/06/15/atandt-sold-out-of-iphone-4-for-launch-day/
I got my order in around 4:28 pm. The confirmation email says this:
Thank you for your purchase from the AT&T Premier Online Store. We're pleased with your choice of AT&T as your wireless service provider.
Pre-orders will be fulfilled beginning June 24, 2010. Orders will ship on a first-come, first-served basis. We will notify you by email when your order ships. Your order may be subject to AT&T eligibility and credit requirements. If we have any questions about your eligibility or your order, we will contact you via email.
Does that mean I'm good? The order status page doesn't have any dates on it.