No. You can get delivery any time of day, but it is not scheduled. If the mail is very heavy (as in volume), then the carriers will be out delivering it until it is all delivered. Sometimes that can be until 11pm. But no, mail is not delivered 24/7. And if you are only talking about one day, why did you include the "7"? (The Post Office DOES deliver 7 days a week - they deliver Amazon packages on Sundays)

The hours for delivery still remain those of normal operation, 8:00 am through 6:00 pm, but the Post Office has expanded the delivery of mail pieces during the month of December. Delivery will be seven days a week until 25 December, with both envelopes and packages on Monday through Saturday, and packages only on Sunday.

http://fortune.com/2014/11/06/usps-to-de...

24/7? no

They never deliver 24/7.