Yes, but it is NOT the gospel of salvation. It is merely an affirmation of Romans 6 and Romans 8; remember this scripture is in
chapter 10 - well after the preceding chapters on baptism and the need for the infilling of the Holy Spirit.
You cannot take one scripture as a stand alone of itself and say that's the gospel. Scriptures unto salvation do NOT contradict or negate each other, especially the fundamental requirements for salvation.
Ye must be born again of water and of the Holy Spirit to enter the Kingdom of God.
Saying some sinner's prayer or saying out aloud that one "believes" in Jesus is not the same.
When one says the sinners prayer acknowledging Jesus as Lord and Savior....the Bible says that God pours His Love into their heart. Another one says that he removes the heart of stone, and puts in one of flesh, giving them a new spirit...so if they receive a new Spirit (which is the Holy Spirit) then they have just been born again of the spirit.