Yes! The gospel saves sinners!

"Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye stand;

 By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.

"For I delievered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; 

 And that he was buried, and that he rose again the third day according to the scriptures:" 1 Corinthians 15:1-4