Well, not quite! At least, that's not quite what the verse says.
What Paul actually writes in Rom 1.16 is that the gospel "is the power of salvation for everyone who believes" - and that makes a great deal of difference!
You see, I think what we usually mean when we talk about the gospel as the power of God for salvation is that it is the power of God to convince people to believe. In other words, that the announcement of the gospel to unbelievers is what causes them to have faith. And, of course, there is truth in that - after all, as Paul puts it in Rom 10.14-15, "how can they believe in one of whom they have never heard?"
However, in Rom 1.16, Paul is saying that the gospel is God's power to bring people who already believe to salvation; namely, to escape from the wrath of God that is being revealed (Rom 1.18). He's not at this point talking about what causes people to have faith, he's talking about people who already have come to faith.
Why does this matter? I think there are 2 reasons.
First, according to the New Testament, the agent who works to bring people to faith is the Holy Spirit. As Jesus puts it in Jn 3.8: "The wind blows where it chooses ... so it is with everyone who is born of the Spirit." Of course, the Spirit uses the announcement of the saving significance of the life, death, resurrection, ascension and return of Jesus Christ; but it is the Spirit who brings new life - after all, he is the Lord, the giver of life.
The difference here is one of control. You see, we are in control of the way we proclaim the gospel. The words we use, the ideas we put together with those words, the force with which we communicate those ideas - these are all decisions we make. And I wonder whether sometimes, when we say that the gospel is the power of God for salvation (in the sense that it is what brings people to faith), what we implicitly are saying is that if only we get the words and ideas and communication right - really, really right, perfectly faithful to Scripture in every way, with no gap or remainder - then people will surely come to faith!
Which then leads to a flip side. Namely, that if people are not coming to believe, it must be because we - or others - have not articulated the gospel accurately enough!
Now, don't misunderstand me. I'm all for accuracy - that is, Biblical faithfulness. Our concern for accuracy must come from a deep devotion to God, so as not to be found to misrepresent him - God forbid!
But there's more to faithful proclamation of the gospel than accuracy, in two sense. On the one hand, accuracy does not replace the life-giving, faith-giving work of the Spirit - he is the one who blows unbelief away, where he chooses. And on the other hand, our proclamation needs not to be merely accurate - although it certainly needs to be that - it also needs to be intelligible. And that means not only linguistically intelligible, but also culturally and conceptually. And that means contextualisation.