Yes and I think that in one of the later Letters, JRRT refers to Auden as one of his great friends, despite them having only actually met on a few occasions. It would seem that their friendship blossomed through correspondence.
Thanks Bb.

Next up, and staying on the WH Auden theme:
In what way did WH Auden expose Tolkien to ridicule and cause him and, in particular, Edith much embarassment?