Beej, you might have missed in my post where I said at the end that faith in Christ produces good works in our lives. If someone claims Christianity and has no fruit in their lives, then yes, that would mean their faith is dead.
It is by abiding in Christ, and He is us, that we can do any good works in our life. But it is not good works that saves us. It is by the gift of salvation, and the indwelling Holy Spirit that we are able to do good works.
Ephesians 2:10
For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them.