No, I don't agree. I have had numerous conversations with Calvinists on this forum and all agree that regardless if one is of the "elect" salvation STILL happens because of God's grace and through faith. The difference is the belief that those who are predestined to salvation do not resist God's grace but they still do have faith. Without faith NO ONE comes to God. I won't presume to explain their doctrine for them, but that is what I have understood them to say. As to the other petals on the tulip, I think even you would agree with more than a few points.
I think that is very incorrect according to the theology.
If one is not elect, salvation does not happen. If one is elect salvation happens. Election by itself determines whether salvation must or can not possibly happen.
Grace, faith are dependent, election the independent cause. One can say what they wish, but this is the theology.