I started thinking about this after reading Rae and Rachel's posts about CW's actual chances in 1806. In ch.4, we are told that "he was, at that time, a remarkably fine young man, with a great deal of intelligence, spirit and brilliancy".
[CW] was confident that he should soon be rich; full of life and ardour, he knew that he should soon have a ship, and soon be on a station that would lead to every thing he wanted. He had always been lucky; he knew he should be so still. Such confidence, powerful in its own warmth, and bewitching in the wit which often expressed it, must have been enough for Anne; but Lady Russell saw it very differently. His sanguine temper, and fearlessness of mind, operated very differently on her.
I think most of us agree that from a practical, logical POV, Lady Russell was perfectly right to worry and try to persuade Anne as she did. On the other hand, when I've come across similar "rags to riches" life stories, the individual involved almost always had the same unshakeable belief in themselves, and the same clear picture of where they wanted to end up, even when it seemed quite impossible, even slightly insane, that it would ever come true. Was CW's success a lucky chance, or at least partly the result of his own self-confidence? I guess that's something that could always be argued back and forth, but I think his self-confidence did affect his ultimate success.