Praise be to Allah.
In my opinion the action mentioned is not permissible, and I do not recall anything of this kind being reported from the Salaf. A person will only be rewarded for what he himself reads or listens to in order to benefit from it. But if another person reads and he does not listen, the reward for that will go to the person who read it. These people are not considered to have completed the whole Qur’aan; but if each person has read a juz’ he will be rewarded for that. But they should not do this; either one person should read and the others listen, or each person should read by himself without making a connection between his reading and that of the others.