Yes. Men with a living faith (cf. James 2:20) are justified, forgiven of their sins, and will reach Heaven, even if they must pass through the purgatorial state first. Men without a living faith will be condemned.
Which would imply that Christ's sacrifice was not enough. I'm sure that would be news to Christ. He was pretty clear that his sacrifice was sufficient. So was Paul. Perhaps they just weren't familiar with Catholic doctrine.