No. You must be born again. If one truly "accepts Jesus as personal Lord and Savior," then one IS born again. That isn't just saying a few words according to a script. It is repenting of sin, accepting the sacrifice of Christ as payment for our sins, and determining to live a life of obedience to His divine will.
It's just easier to say "saved."
"...of water and the Spirit." Meaning Baptism.
"Go and make disciples of all the nations, baptizing them in the name of the Father, Son and Holy Spirit."
If one truly "accepts Jesus as personal Lord and Savior," then one IS born again. That isn't just saying a few words according to a script. It is repenting of sin, accepting the sacrifice of Christ as payment for our sins, and determining to live a life of obedience to His divine will.
Can someone who is "born again" by your definition ever fall away?