I say, and with God's success: It is not permissible for him to do that; because it is a condition for the validity of the intention in tayammum that he intends a specific act of worship that is only valid with purification, and reading the Quran from memory is a non-specific act of worship that is valid without purification. Refer to: Al-Durr Al-Mukhtar 1: 165, Al-Radd Al-Mukhtar 1: 165, and Al-Iyadah Q6/B, and God knows best.