Do you mean that faith is necessary in order to become saved, or is it the result (byproduct)of having been saved?
Salvation is, in itself, is a multi-faceted plan... as you well know. Salvation of the Elect is assured from all Eternity and is in the hands of the Eternal God. The Father purposed it, The Son carried it out and The Holy Spirit applies it.
To say there could be NO Salvation without FAITH is a truism. However to say, that one who is written in the Lamb's Book of Life, will not be given this FAITH and exercise it, would be a lie. The points of Salvation are these:
From mans perspective:
1) Hearing or reading the revealed Word of God.
2) Believing or exercising faith - they are one and the same really.
3) Repentance
4) Laying hold of Christ as the only Savior
5) Finding or being led to a local assembly.
6) Following after Christ in Baptism, as the first obedient act out of a good conscience.
7) Continuing in the fellowship of the Saints, centered around sound Doctrine. For in sound Doctrine is the Truth of God which points to our Lord and Savior. It prepares the "Bride" for meeting her "Bridegroom".
Points number 5 and 7 are getting more and more difficult in these later days. One may find themselves in a famine for the True Word of God where they live. I once heard of a young lady, over in England, that tried for two years to find a place to call home. She did finally find a small assembly where she could accept their teachings.
From God's perspective:
1) A decision to create and make known His Glory.
2) Having a plan to redeem some, from a fallen condition, knowing that creation will be cursed because of sin, even before He created it or anyone.
3) Choosing His own Son to be it's Redeemer before anything is created.
4) Having an intimate knowledge of the ones He will chose in Christ before He creates anything.
5) Giving them to His Son, in the Covenant of Redemption, (Lamb's Book of Life), as a love gift to Redeem. This too before the foundation of the world.
6) The Holy Spirit goes to each elected individual, at the appropriate time, to give them a new spiritual birth. This alters their fallen nature and gives to them each spiritual gifts to aid them along the way. It has been the same for the Old Testament Saints as the New. This was based on God the Father's sure knowledge of His Son's redemptive work being carried out. What God plans He does.
7) The Holy Spirit, in the role of comforter, ( New Testament age), indwells the believer and guides his/her thoughts, about the Scriptures they know, in the direction of Jesus Christ as the one and only Redeemer.
8) The Savior carries this one all the way to the finish line and nothing can prevent this one from successfully crossing it. This one joins the Worship in Heaven, singing songs, giving praise to the Lamb and will be with the Lord forever, apart from sin in his/her glorified body.
I know this is more than you were asking about but I just wanted to say it.