In a Linguistics SE question on loanwords from Japanese into Chinese, it was said that the Chinese import the kanji and use their own reading thereof. So words in kun'yomi are unrecognizable in speech. It got me thinking about ateji: these must make messy loanwords. But since the on'yomi is close to the Chinese readings the Chinese and Japanese versions may sound alike so long as the on'yomi is used.
So, at long last, my question: are there kun'yomi ateji?