Does Paul teach believers that salvation has nothing to do with behavior?

Thank god!

Yes, people's salvation has nothing to do with behavior!

Ephesians 2:5: When we die in our sins, let us live with Christ. You are saved by grace.

Excuse me: Can the dead save themselves? Don't! God wants us to live with Christ first, so we are saved by grace!

Ephesians 2:8: You are saved by grace and faith. This is not from yourself, but from God. Nor out of deeds, lest anyone boast.

In this matter of salvation, no one has any credit, which is entirely made by God!

Hallelujah!