Listening to the Quran is prescribed in Islam, so yes it earns good deeds.
Allah commands listening to the recitation of the Quran:
وإذا قرئ القرآن فاستمعوا له وأنصتوا لعلكم ترحمون
So when the Qur'an is recited, then listen to it and pay attention that you may receive mercy.
— Quran 7:204
The Prophet ﷺ used to listen to the Quran:
عن عبد الله، رضى الله عنه قال قال لي النبي صلى الله عليه وسلم اقرأ على القرآن . قلت آقرأ عليك وعليك أنزل قال إني أحب أن أسمعه من غيري
Abdullah (ibn Mas'ud) said: That the Prophet (ﷺ) said to him, "Recite the Qur'an to me."
Abdullah said, "Shall I recite (the Qur'an) to you while it has been revealed to you?"
He said, "I like to hear it from others."
— Bukhari
And the Sahaba and Tabieen used to do the same:
أن جماعات من السلف كانوا يطلبون من أصحاب القراءة بالأصوات الحسنة أن يقرؤوا وهم يستمعون وهذا متفق على استحبابه
The Salaf used to ask those who recited beautifully to recite the Quran so that they could listen. And this is recommended by agreement.
— Tibyaan fi Adaab Hamalat al-Qur’an