What is the ruling on one of the worshippers performing the Iqamah for prayer due to the Imam's delay, then the Imam entering and leaving without praying with the congregation?

The Imam leaving the mosque after the iqama for prayer is incorrect. In this situation, the prayer is valid according to the majority of scholars. The Imam's departure is considered disliked (makruh) by some scholars and forbidden (haram) by others, unless there is a valid excuse.

The statement by some Hanbalis that the prayer is invalid if someone other than the regular Imam leads the prayer without his permission might be what the Imam relied upon for his departure. However, the opinion that the prayer is valid despite the sin is stronger, because prohibition does not necessarily entail the invalidity of the prayer.

It is more appropriate for the Imam to join the prayer with the congregation than to leave the mosque, in order to preserve the congregation and avoid disunity.