Whisper, I am game on responding to your post and hopefully it will clear up a few misconceptions you have about Catholics and their beliefs.
Catholics also believe this. So we are in agreement here.
We actually teach that Christ's sacrifice was "super-"sufficient in paying for our sins. So we are in agreement here as well.
We are in agreement here as well about Jesus' suffering and death has appeased God's wrath against sin, in that eternal punishment is atoned for. But for our sake, God has allowed temporal punishment to remain as a means of disciplining and correcting us. Hebrews teaches us:
Heb 12:
[5] And you have forgotten the consolation, which speaketh to you, as unto children, saying: My son, neglect not the discipline of the Lord; neither be thou wearied whilst thou art rebuked by him.
[6] For whom the Lord loveth, he chastiseth; and he scourgeth every son whom he receiveth.
[7] Persevere under discipline. God dealeth with you as with his sons; for what son is there, whom the father doth not correct?
[8] But if you be without chastisement, whereof all are made partakers, then are you bastards, and not sons.
About the question you asked. I key point should be that those that are purged are already saved as you understand it.
Catholics do not believe that we are saved by our works. We are not Pelagianists. We believe as you have professed that we are saved through the cross of Christ. Without this redemptive act by Christ we would have no chance for salvation. In fact the council of Trent session 6 on Justification points this out very well:
CANON I.-If any one saith, that man may be justified before God by his own works, whether done through the teaching of human nature, or that of the law, without the grace of God through Jesus Christ; let him be anathema.
CANON II.-If any one saith, that the grace of God, through Jesus Christ, is given only for this, that man may be able more easily to live justly, and to merit eternal life, as if, by free will without grace, he were able to do both, though hardly indeed and with difficulty; let him be anathema.
CANON III.-If any one saith, that without the prevenient inspiration of the Holy Ghost, and without his help, man can believe, hope, love, or be penitent as he ought, so as that the grace of Justification may be bestowed upon him; let him be anathema.
CT06
No.