Is reading the Quran aloud and continuously in the mosque, in a way that prevents concentration during the "Tahiyat Al-Masjid" (mosque greeting) prayer, considered part of the Sunnah?

It is not permissible to raise one's voice with the Quran in the mosque, as this leads to disturbing those praying and those reciting. This action is not from the Sunnah, and it is even more prohibited to raise one's voice with anything other than the Quran.