I just talked to the shipping guy at my office and he said that UPS will accept overnight shipments as long as it is in by 5pm (I know this is probably common knowledge but don't make fun of me), so I'd say there is hope!
I'm assuming that Apple sent out the dreaded email of death to anyone with the 4/24-5/8 shipping window and is still at processing.
That hasn't been the trend based on this week's events, but people can overnight stuff from Alaska if they get it in the afternoon, so technically it's possible!
I ordered my 38mm SG at XX:02:24am (with 4/24-5/8 delivery) and didn't receive the email of death, so I don't know what's up with that.