Yes, his faith is 'dead' in Genesis 15:6, because by pure definition "faith if it has no works, is dead, being by itself." (James 2:17 NASB italics in original). And we know his work that came later in Genesis 22, and which made his faith 'alive', did not make his faith in Genesis 15:6 a justifying faith because it plainly says his faith there in Genesis 15:6 was a justifying faith.
If dead faith by definition is 'faith without works', as it surely is (James 2:17 NASB), then, yes, before Abraham's faith came to completion (that is, was fulfilled) it was dead, not having works.
I know that's probably a scary thing to say, but it's only scary because we've been conditioned to automatically think that dead faith is categorically and without exception, all of the time, a false faith. But that's simply not true. Dead faith is simply faith that hasn't acted. Whether or not the faith is genuine determines if it really can, or will act or not. James calls it 'useless' faith (James 2:16,20 NASB). In the example he gives, it's no use to the brother or sister in need (James 2:16 NASB). That hardly means it can't be genuine. It means it's no use for anything, even salvation (I didn't say justification) until it finds fulfillment in some kind of manifest obedience to validate it as genuine.
Work proves the existence of faith. The work produced can determine whether the faith that produced it is a justifying faith or not. For example, love exposes justifying faith in a person, while simply going to church, or getting circumcised, or giving money to the church does not--but it doesn't mean those things can't ever be motivated by a genuine justifying faith in Christ. In Abraham's example, by the nature of what it meant to put Isaac on the altar, believing he would die yet live again, that work did expose his faith as the faith that justifies. This in no way defeats the truth that faith is dead until it does something. Even Abraham's faith was dead, being useless to show him as having the righteousness that comes by faith, until it did something commensurate with what it believed when the opportunity arose.
No question about it. If someone's faith can't produce a change of nature, that faith can not save that person on the Day of Wrath because it can't produce the expected obedience by which God measures justifying faith. It was either never the faith that justifies to begin with, or, the faith that justifies ceased somewhere along the line. That 'faith' is useless. It can not save a person. It can't justify the person who has it, nor can it produce the required works that validate it as able to justify. And it sure doesn't help the people around us live better lives.
It's really quite simple: Faith does the justifying--the making righteous--all by itself, apart from what it does. And we know that faith is able to justify by what it does. What it does is what God will use on the Day of Judgment to determine if you do indeed have the righteousness of Christ and, therefore, eligible to enter the kingdom, because that is how justifying faith (the faith that makes you righteous in God's sight) is recognized and identified. It's that "faith working through love" being the only thing that means anything toward justification thing that Paul talks about (Galatians 5:6 NASB).
Yes. That is true. Faith that doesn't justify is dead faith because by what it means to be justified (made righteous) it can't produce the work of the new nature. The problem with what you're saying is, we can't turn 'faith that doesn't justify is dead faith' around and say 'faith that is dead doesn't justify'. We know that can't possibly be true because Abraham's faith was dead (being without works) when he had it in Genesis 15:6 NASB. ALL faith starts out that way. What is important is that it not remain dead (absent of work) so that faith can then save us.
You are making the erroneous inference that work completed points back and makes the faith that produced it now able to justify. And I think you're doing that because you and a lot of other people, me included, have erroneously defined 'dead' faith as the faith that can not justify. But actually James' definition of 'dead faith' is 'faith that has not acted' and is, therefore, useless in actually accomplishing something. That doesn't mean it can't, or never will act, accomplishing something. And it doesn't mean it's not a justifying faith. We know that because Abraham did not 'complete' his justifying faith in Genesis 15:6 until much later when he sacrificed Isaac on the altar in Genesis 22:9-10, yet his then 'dead' faith in Genesis 15 justified him, nonetheless.