No
Saved means forgiven of sin
Salvation is offered to ALL, of they only accept it
And if they accept it, they are privileged.
I think the problem is that typically privilege is bestowed. But in this case, the saving is bestowed, and privilege comes only with acceptance of salvation.
It is almost circular logic.
From the Bible:
“Many are called; few are chosen.”
I think we will be astounded at our moment of death (since many refuse the call.)