Yes, and I would say actual faith is a cognitive error more akin to deja-vu than double think, in that it is a feeling of knowledge for which adequate logical justification may not exist. A friend of mine once said, "I'm sorry that I'm so bad at explaining this [the existence of God], but I just know it, and once you do too, you'll understand."

People can have experiences of faith in non-religious contexts, such as having faith (a sense of certainty or foreknowledge) that a critically ill loved-one will pull through. Intuition and gut-feelings maybe considered faith-light, but I think certainty is part of the faith experience, and just because that certainty is false, doesn't make the feeling any less real.