Brilliant, I say!
But I think
Inzil has a good point here - would Tolkien not mention the origin of the word somewhere if it had been the case? Then again, it sounds veery unlikely that it would be completely unrelated (especially given his knowledge). Unconscious influence would therefore seem the most logical (like that he had heard the word somewhere, forgot about it and later simply used it, thinking it was "his") - unless the Prof wanted this to be his own private secret, hidden from his readers and others?
For that matter, this all makes the sentence
"In a hole in the ground there lived a hobbit" much more dadaistic by origin than it would seem