I don't think so. Now I agree that the "righteousness through faith" theme is there, but I don't think it is where Paul rooted his hope, either for himself or for his churches. It wasn't what kept him going.
"I consider that the sufferings of this present time are not worth comparing with the glory about to be revealed to us.19 For the creation waits with eager longing for the revealing of the children of God;20 for the creation was subjected to futility, not of its own will but by the will of the one who subjected it, in hope21that the creation itself will be set free from its bondage to decay and will obtain the freedom of the glory of the children of God.22 We know that the whole creation has been groaning in labour pains until now;23 and not only the creation, but we ourselves, who have the first fruits of the Spirit, groan inwardly while we wait for adoption, the redemption of our bodies.24 For in* hope we were saved. Now hope that is seen is not hope. For who hopes* for what is seen?25 But if we hope for what we do not see, we wait for it with patience." -Romans 8:18-25What kept him going? It seems that "obtain[ing] the freedom of the glory of the children of God" was fairly important to Paul. And what does that mean? I would argue resurrection and eternal life.
"But in fact Christ has been raised from the dead, the first fruits of those who have died.*21 For since death came through a human being, the resurrection of the dead has also come through a human being;22 for as all die in Adam, so all will be made alive in Christ.23 But each in his own order: Christ the first fruits, then at his coming those who belong to Christ." -I Corinthians 15:20-23
"I want to know Christ and the power of his resurrection and the sharing of his sufferings by becoming like him in his death, if somehow I may attain the resurrection from the dead." -Philippians 3:10-11
"Have nothing to do with profane myths and old wives' tales. Train yourself in godliness, for, while physical training is of some value, godliness is valuable in every way, holding promise for both the present life and the life to come." -I Timothy 4:7-8
"Paul, a servant of God and an apostle of Jesus Christ, for the sake of the faith of God's elect and the knowledge of the truth that is in accordance with godliness, in the hope of eternal life that God, who never lies, promised before the ages began...." -Titus 1:1-2
"This Spirit he poured out on us richly through Jesus Christ our Savior, so that, having been justified by his grace, we might become heirs according to the hope of eternal life. -Titus 3:6-7All throughout Paul's letters we can read his language of eternal life, but if we stop there we're left with a rather lopsided picture of Paul's hope, because without a more important event, resurrection, as Paul seems to understand it, never occurs.
"Set your minds on things that are above, not on things that are on earth, for you have died, and your life is hidden with Christ in God. When Christ who is your life is revealed, then you also will be revealed with him in glory." -Colossians 3:2-4
"For the Lord himself, with a cry of command, with the archangel's call and with the sound of God's trumpet, will descend from heaven, and the dead in Christ will rise first. Then we who are alive, who are left, will be caught up in the clouds together with them to meet the Lord in the air; and so we will be with the Lord forever." - I Thessalonians 4:16-17
"In the presence of God, who gives life to all things, and of Christ Jesus, who in his testimony before Pontius Pilate made the good confession, I charge you to keep the commandment without spot or blame until the manifestation of our Lord Jesus Christ, which he will bring about at the right time--he who is the blessed and only Sovereign, the King of kings and the Lord of lords." -I Timothy 6:13-15
"From now on there is reserved for me the crown of righteousness, which the Lord, the righteous judge, will give me on that day, and not only to me but also to all who have longed for his appearing." -II Timothy 4:8
"For the grace of God has appeared, bringing salvation to all, training us to renounce impiety and worldly passions, and in the present age to live lives that are self-controlled, upright, and godly, while we wait for the blessed hope and the manifestation of the glory of our great God and Savior, Jesus Christ." -Titus 2:11-13Jesus's life, kingship, and return. I don't hear that much in most modern churches. Quite a bit of modern theology is built upon the hope of going to heaven when we die. That hope is surprisingly absent in Paul's letters. He doesn't speak much at all about heaven or what happens when we die. What Paul talks about is what happens when Jesus returns and we have life again, this time eternal life. If you want to see more evidence of this in Paul's thought, feel free to look at more from I Corinthians 15 & 16, Ephesians 4:29-30, I Thessalonians 3:13, II Thessalonians 1:6-10, II Timothy 2:3-7, 16-18; this strand of Paul's thought is everywhere.
I think the difference between Paul's hope and the hope many congregations are trying to give their members is rather striking. Thinking that the hope of Christianity is going to heaven when we die makes life nothing but a test. It devalues all things physical and this worldly. It creates a gnostic vision where nothing good can exist until we die and are set free. Paul seems to think that through the death and resurrection of Jesus, and his reign thereafter, this life does have a purpose. We have been set free to experience life the way God intended it, in a community that God has created, called the Church. However, as is often times the case when two groups make mutually exclusive claims, the "world" or the "flesh," as Paul puts it, is opposed to God's will in us, as it was to Christ. So, as Jesus was persecuted, so too will we be persecuted. Along those lines, as Jesus suffered for a world that hated him, we must suffer for a world that hates us. But no matter what happens, our hope is that one day Jesus will return, and on that day everyone must admit that he is the Christ, the one King of kings and Lord of lords. On that day, true life, flowing from the eternal source, will bring all of Christs's people back to life and transform the mortal into the immortal. That is a much richer vision of our final hope than "going to heaven," at least in my opinion.
If we want our churches, and the individuals that make them up, to be more effective and essential in our communities, maybe it is time to catch a glimpse of Paul's hope. After all, if you don't know where you're going, how will you know if you're headed in the right direction?
Stopping point: Philemon