I don't think so...
A person may decide to receive Christ out of entirely selfish motives...because they do not want to go to hell, for example.
If for other reasons a person comes to Christ (because they experience God's love coming from Christians, or because they become convinced intellectually that the gospel is true), even that is not something that is in itself good in the heart of the person who receives. They simply become convinced of the truth because the evidence is there. This does not necessarily indicate goodness in the heart of the person who becomes convinced.
Also, as concerning surrender to the Lordship of Christ, I am not denying that there is a drawing effect that must take place for a person to make that decision. Perhaps faith comes first and then surrender; but that salvation is there in the surrender of the heart to Christ. In such a case it is not faith that saves; even though the Bible clearly teaches that we have access by faith into this grace wherein we stand.
Perhaps it is only a faith that becomes fully matured that even has the power to save anyone.
It goes back to whether a person is saved by grace through faith so that they can have faith...the reality of the matter is that they already have faith, and it is that which saved them!
I would postulate that it is only a living faith that saves...and that such a faith always includes surrender to the Lordship of Jesus Christ.
So, perhaps a person can have faith that doesn't save them, or that they can be saved before they ever have faith in the Lord...since as
@Dave L contends, faith comes after salvation and not before. And if that is the case, I can have salvation without faith in Jesus...
Strange brew indeed...