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woman wins a million dollars in a lottery. When she goes in to collect her winnings, she signs a form in order to transfer the money over to her possession. Is her signature the cause of her getting a million dollars?
In one sense, yes -- the signature was necessary for her to take possession of it; if she had not signed she would not have received it. Her signing the paper was the formal act that caused the conclusion of the money-winning process.
In another sense, no -- there is no "inherent connection" between signing a piece of paper, and collecting a million dollars. The true cause was the lottery system, and the signature a nigh-arbitrary symbolic act that more-or-less signified acceptance of an already-accomplished event. The woman does not win a million dollars every time she signs a piece of paper; and we would not say that her signature made her "deserve" the money, if the lottery system hadn't already been in place.
This is how we ought to think about God's Grace. Our Heavenly rewards are a pure gift from God -- we do not earn them through our actions. However, our actions are a sort of symbol of our acceptance of God's mercy. If God pours out his love on us, and we do not respond with love to Him and to our neighbor, we are like the lottery winner who doesn't sign the paper. Acts of love are insufficient, considered on their own, to make us worthy of Heaven; but they act as a "seal" on our relationship with the Lord.
However, in God's plan, every part of the economy of Grace is imbued with higher meaning -- and therefore, of course acts of faith and charity have a much more meaningful, and less arbitrary, character than the signing of a document.