Is it necessary to have sex on the day of marriage?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Basically all rulings should be derived from the Islamic Sharia. So, no decree could be given except if there is evidence in the Qur'an, Hadith, or the consensus of Muslim Ummah or through sound analogy.
However, we do not know any evidence that proves that having intercourse is compulsory in a given night, on the Eve night or any other nights.
Allah knows best.