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 cannot be performed except with purification, and entering the mosque is not a specific act of worship in itself, but rather it is dependent on something else. However, it is permissible for him to enter the mosque with this tayammum. Refer to: Al-Durr Al-Mukhtar 1: 165, Al-Radd Al-Mukhtar 1: 165, and Al-Iydah Q6/B, and God knows best.