Certainly there is an aspect of the Gospel that means just that, but I would suggest that the Good News associated with Jesus means much more than this.
It is important to stress, as Paul would do himself were he not so muzzled by his interpreters, that when he referred to "the gospel" he was not talking about a scheme of soteriology. Nor was he offering people a new way of being what we would call "religious". Despite the way Protestantism has used the phrase (making it denote, as it never does in Paul, the doctrine of justification by faith), for Paul "the gospel" is the announcement that the crucified and risen Jesus of Nazareth is Israel's Messiah and the world's Lord. It is, in other words, the thoroughly Jewish, and indeed Isaianic, message which challenges the royal and imperial messages in Paul's world.
The world's rightful King has come into this world through the nation of Israel. He has come to rescue us from evil and set the world to rights. That is Good News! Yes, the fact that we are saved from our sins is tied up in this, but it is not the entirety of what the Gospel is about. In other words the King has come and now is the time to pledge your loyalty to Him.
Paul's Gospel and Caesar's Empire | N. T. Wright