All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
In general, gathering to recite the Quran is permissible. The Prophet said: "Whenever a group of people assemble in one of Allaah's houses (mosques) for the sake of reciting the Book of Allaah (Quran) and studying it among themselves, they will be blessed with the decent of tranquility…'' [Muslim]
However, we do not know any evidence about the method that is mentioned in the question, and that is not considered as finishing the recitation of the Quran. All good lies in following our righteous predecessors . It is confirmed that the Prophet said: "Whoever introduces into this faith of ours that which is not part of it, it will be rejected." [Al-Bukhari and Muslim]
Allaah Knows best.