I think you have a good point, and the answer is yes: I would live a life of faith and works in either case. There could be a difference in the long run, though. If the CC position ultimately leads me to lean more on my own faithfulness/cooperation with grace than on the redemptive work of Christ, then that would be a problem. I’m not saying that would happen for sure, but it’s something I’m concerned about.
I think this would help you immensely in your question/concern here:
catholiceducation.org/articles/apologetics/ap0091.html
From which I will quote/cite:
On the one hand, as an Evangelical Protestant, I had firm convictions about the finished work of Jesus Christ; that He accomplished our redemption on the cross. Those convictions I still hold fast to. Every Christian, every Catholic must. The work of our redemption is accomplished. It is finished. But the application of that redemptive work of Christ by the Holy Spirit is another matter, one that I did not really come to grips with because it involves suffering which nobody wants to come to grips with — either suffering in this life or suffering afterwards to expiate or to repay or to provide restitution for the effects of sin.
But that distinction is going to be crucial from the beginning of our time today until the end — that Christ has accomplished our redemption. It’s over and done with. He has finished it. But then He sends the Holy Spirit to apply it, and the application of redemption is just as essential.
Furthermore, we’ve got to clarify the fact that it is not to make up for Christ’s unfinished work. I’ve already said that, but that, too, is a common misconception that continually needs clarification. There’s nothing inadequate about the work of Christ. It’s finished, but it needs to be applied…The essence of Christianity is Christ reproducing His life, His suffering, His death and then His resurrection in glory in us. That is the essence of Christianity…We are called to share in Christ’s suffering so that we could share in His glory. Some of us take short cuts, don’t we? But God will not abandon us because He loves us immature children too much, just the way we are, but too much to let us stay that way…The more suffering that you endure in faith and hope and charity, the more God’s love is being revealed to you…hat’s what it means to be united in him. That’s what the whole significance of our baptism is. Paul says in Romans 6 that because we have been baptized, we have died to sin. When James and John brought their mother to kind of lobby for the right and the left seats in glory, he said, “Are you willing to be baptized with the baptism with which I have to be baptized?” So what did He associate baptism with? An ordeal of suffering. Christ said, “I come to baptize with fire.” I’ve got to tell you, a lot of people are making salvation out to be heavenly welfare. No wonder it sells. I could fill a church in a matter of months, it I was preaching nothing but welfare from heaven for nothing we do. We don’t have to suffer. We don’t have to work. We don’t have to obey. We should, but we don’t have to. That’s wrong, but it will sell in this century and in every age.
Nobody is going to say, “Christ has died on the cross; therefore, we don’t need faith.” Of course we need faith. Well, if we need faith, is it because Christ’s work isn’t finished? After all, He says, “It is finished.” Why do we need faith? We’re all saved. Nobody says that. Even non-Catholics say, “We have to have at least faith.” Well, if we have to have anything besides the cross of Christ, if we have to have personal faith, and that doesn’t undermine the work of Christ, then we have to ask, why? Well, it’s because the Holy Spirit gives us faith and then hope and then charity and the capacity to sacrifice and suffer. And how crucial it is that we willingly cooperate with that grace…Now does he mean that Christ died a little too quickly? He needed a few more hours? No. It means that Christ’s suffering and death must be reproduced and filled up in the Church and if some are slacking off, that means others must become more like victim-souls, willing to bear a greater burden, willing to shoulder with love, as Galatians 5 speaks about the love, “Love bears one another’s burdens.” …
Now what does this mean, that Christ has not paid for our sin? Of course not. It doesn’t mean that. Christ has paid once and for all for our sin. His death is the ultimate satisfaction and price for our redemption, **but His life and His death must be lived out in us. That’s why we need to pick up our cross, and we need to imitate Christ. Did you catch that? We don’t suffer because Christ’s sufferings weren’t enough. We suffer because Christ’s life must be reproduced in us. It is finished. It is accomplished, but now it must be applied. **The work of the third person of the Holy Spirit is New Testament history, is personal history.