That's when my oldest started sleeping through the night. As long as they're still growing & eating well, have plenty of wet diapers, and don't have anything that @shelbyann said, you're good :D
Most definitely! My son slept all night from day 1. As long as the baby breathes fine, doesn't seem blue, lethargic, or anything alarming like that you're fine. Just a lucky momma! :)