Is it permissible to invoke blessings upon the Prophet (peace be upon him) if the Imam recites the verse: "O you who have believed, invoke upon him blessings and grant him a thorough [period of] greeting"?

If you are behind the Imam in a loud prayer, you must listen to his recitation and not speak, not even with dhikr or supplication, because of Allah's saying: (And when the Qur'an is recited, listen to it and pay attention), and because of the hadith: "When he recites, then listen." As for outside of prayer, during a Friday or Eid sermon, or if you hear the Qur'an, it is permissible for you to send blessings upon the Prophet, peace and blessings be upon him.