Is it permissible for someone who entered the mosque at the time of the 'Asradhan to pray immediately without waiting for the Iqamah due to being busy?

A Muslim should pray in congregation at the mosque if he is able. If there is an excuse, then there is no harm in him praying individually before the congregational prayer and then leaving. Among these excuses are: fear for one's property, the presence of a sick person who must be accompanied, or an appointment that would be detrimental to miss.