First of all, it's important to realize that there is a certain danger in trying to prove an author's worldview from a single work of fiction or poetry. An author may be assuming a point of view just for that work that is not his own. Or, in the case of A Christmas Carol, the work may be a fantasy and therefore may represent a stylized version of the author's views which cannot necessarily be taken literally. With that said, there are a few interesting reflections within A Christmas Carol that pertain to religion and the afterlife.
The most direct correlation the novella gives us between this life and the next is through the visit of Jacob Marley's ghost. Marley explains that he wears the chains he forged in life, and that since his spirit did not go beyond the walls of his counting house when he was alive, he is sentenced to roam the Earth in the afterlife wearing his heavy chains. His punishment is the "incessant torture of remorse." Marley states that what he should have tended to during his life were "the common welfare . . . charity, mercy, forbearance, benevolence." He mentions the Christmas star, but only in a symbolic sense that he should have been led to help the poor at Christmas time. In this passage there is no real mention of religious faith, only of kind deeds and providing for the needs of the unfortunate.
The phantoms that Scrooge views outside his window at the end of Stave I are reiterations of Marley's ghost. They, too, are suffering from the remorse of having squandered their opportunity to help people while they were alive.
Another interesting passage that connects this life with immortality is in Stave IV where Scrooge is viewing the dead figure in his bed. In a paragraph that is somewhat mysterious as to its speaker and meaning, we read, "Strike, Shadow, Strike! And see his good deeds springing from the wound, to sow the world with life immortal." This seems to be saying that if the dead man was found to have done good deeds before he died, this would result in immortality. Does that mean immortality for the dead man? Or for mankind? One could interpret it either way, perhaps, or even both.
In the scene where Tiny Tim has died, there is no mention of his being in Heaven. There is a quotation from the Bible: "And he took a child, and set him in the midst of them." It is unclear who speaks those words. This is from Jesus' sermon on the child text. The point of that message from Jesus is that the person who wants to be the greatest in the Kingdom of God must be the servant of all (Mark 9:33 - 37). This is certainly consistent with what Marley's ghost was telling Scrooge.
Finally, in Stave V, when Scrooge has become a changed man, he begins showing generosity to everyone and taking pleasure in the people of London. Then he goes to church. Nothing else is said about religion per se. He became a good man. And the book ends by invoking God's blessing.
Based on the evidence from this novella alone, it would seem that in Dickens' view, one can be a good man and qualify for immortality by serving others whether or not one is religious.