The answer depends on how you define "Blessing" and in what context it is used. One on hand, we can do nothing to earn God's grace. Grace is the undeserved blessing of God. On the other end, God rewards us for being faithful to Him and this could be called a blessing as well. So, the answer very much depends on how the word is used, and in what context.
All the blessings that any of us receive from God are ultimately and only the result of the cross of Christ. There is nothing we can do to earn the favor of God in any way. God loves us and blesses us not because of who we are or what we can do, but because of who He is and how great His love is for us.
Once we are redeemed, we can honor God by being faithful to His word and by preaching the gospel. We are blessed by God in doing this, but the blessing is not a contributing factor towards salvation. Instead, this blessing is a result of our salvation and can also be a result of simply obeying God.