The Bible states that Noah did keep his covenant with God.
* Genesis 6:9 describes Noah as "a righteous man, blameless in his generation; Noah walked with God."
* Genesis 9:1-17 details the covenant God made with Noah and his descendants after the flood. This covenant included God's promise never again to destroy all life with a flood, symbolized by the rainbow. There's no indication that Noah broke any part of the agreement on his end.
Therefore, according to the biblical account, Noah was righteous and kept the covenant God established with him.