Did T.S. Eliot believe knowledge brought us closer to enlightenment?

No, he did not. Eliot was opposed to the enlightenment. He believed that the breakdown of the whole to reach the sum of its part (enlightenment breaking down the universe into small pieces of facts) is the opposite direction that humankind needs to go because it separates science from God. Instead, we should take what we know and build toward the "invisible light", God, who understands the universe perfectly.