Praise be to Allah.
I put this question to our shaykh, ‘Abd ar-Rahman al-Barrak (may Allah preserve him) and he said:
If the speaker means the Qur’an which is the word of Allah, and not recitation, then this comes under the heading of idle speech, because the virtue that results from the words of Allah is by the grace of Allah, such as if one said: By the grace of Allah then by virtue of His beautiful names. That does not make sense, so it is better not to say it.
But if he meant recitation which is a person’s action, then it may mean something, but it is better to attribute the blessing to Allah alone.
And Allah knows best.