Yes, and as an Oxford philologist, Tolkien knew what allegory was. I would say that "allegory" isn't really the right world to describe his works; better to say that they had strong Christian themes.
Yes, Tolkien rejected simple minded allegory, where this stands for that, and so forth. He thought that C. S. Lewis was too obvious, with figures like the lion in his children’s fantasies.
But he didn’t reject the basic Christian principles that underlie his fantasies. For instance, the Silmarilion is not based obviously on the story of Adam and Eve and the serpent, but when you reach the last sentence it becomes evident that you have read a version of the story of the Fall.