We don't have a will that can bring salvation about, no. It's not in your capacity, and it's an incapacity of will, not an incapacity to decide.
As you've pointed out, so you must realize, the dialogue is limited, and the comment is limited.
The question of freedom has been tripartite for centuries, and so the question and its answers are ambiguous until the concept of free will is better defined.
For those who view free will as the ability to do what you want, Calvin has already agreed with that view. And our wills are all sinful, so herein is the highway to Hell.
Of course ..and I agree we cannot "will" salvation and get it... cause it is God who grants it not us... The synergy part is what is needed (for us) like a consent so that God can act in our lives. The gift is all God's... He is the one who bestowes it to us. Our part is though that of "remaining in Him" as "He remains in us" as it says in the parable of the vine:
4Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.
This is the perfect example of how we need to sustain a relationship with Christ in order to "bear fruit" ...
John 15 1-14
1I am the true vine, and my Father is the husbandman.
2Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit.
3Now ye are clean through the word which I have spoken unto you.
4Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.
5I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.
6If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned.
7If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you.
8Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples.
9As the Father hath loved me, so have I loved you: continue ye in my love.
10If ye keep my commandments, ye shall abide in my love; even as I have kept my Father's commandments, and abide in his love.
11These things have I spoken unto you, that my joy might remain in you, and that your joy might be full.
12This is my commandment, That ye love one another, as I have loved you.
13Greater love hath no man than this, that a man lay down his life for his friends.
14Ye are my friends, if ye do whatsoever I command you.
As we can see there is always a "synergy" if you "keep my commands" then you shall abide in my love...etc. That proves that man has to consent to the command of Christ to be "in the vine" with Chrsit and not be cut of.