We actively see owls arrive at various times throughout the day at both Hogwarts, as well as at peoples homes.

Harry received mail from Sirius, and Charlie Weasley at Hogwarts during non-breakfast hours. 

> The clock on the wall had just chimed midnight when the portrait hole burst open. Ron appeared out of nowhere as he pulled off Harry's invisibility cloak.
There was a tap on the dark window. "It's Hedwig!" said Harry, hurrying to let her in. "She'll have Charlie's answer!"

Hedwig in book 3 brings Harry presents at 1 am on his birthday.

> Silhouetted against the golden moon, and growing larger every moment, was a large, strangely lopsided creature, and it was flapping in Harry's direction.


So it appears while typically official mail tends to arrive during the breakfast window, mail does not have a required time to arrive.  

Examples of official mail that arrives at breakfast.

1. Hogwarts acceptance letters. In Chamber of Secrets they arrive during breakfast after harry arrives in the Burrow. 
2. Daily Prophet.
3. Packages from mail order companies, Harry's nimbus 2000, and Firebolt.