In the Ottoman-Safavid case (and potentially in the others as well) propaganda absolutely was used. Ottoman writers emphasized the heretical nature of the Safavids, and depicted them as the absolute enemy of Sunni Islam. In fact, the politicization of Sunni Islam by the Ottomans was in large part tied to the need to create anti-Safavid propaganda, as Kaya Şahin notes (71-2):

"In an age when religion was radically politicized and became a constituent part of imperial ideologies, matters of doctrine ceased to be limited to scholarly circles and produced wider repercussions, drawing both larger numbers of followers and the scrutiny of political authorities. The first decades of Süleyman’s rule witnessed attempts by the political center to create an “official” version of doctrine and the circulation of alternative political theologies and criticisms. The political center presented the sultan as, alternatively, the caliph of Sunni Islam, a messianic conqueror with a claim to universal sovereignty, and the renewer of Islam (mujaddid)."

In analyzing the works of Celalzade Mustafa (Süleyman's chancellor for much of his reign), he has this to say (190):

Relinquishing the earlier image of the warrior-caliph, Süleyman’s caliphate now relies on the restoration of peace and justice in Muslim territories occupied by heretics. Motivated by Safavid claims of velâyet ve kerâmet (sanctity and miracles) and the support of the Twelve Imams, Mustafa offers Süleyman as the only ruler to display signs of sanctity and presents his march from Istanbul to the East with such a large army as his miracle. He laments the fact that the Safavids did not face the Ottoman army in open battle; otherwise, he says, the Ottomans would finally prove that they are the true bearers of sainthood and workers of miracles. The conquest of Baghdad and its vicinity is yet another miracle, according to Mustafa, and one of the signs of the End Time.

This sort of propaganda was meant to depict Süleyman as the rightful ruler of the Muslims, leading the forces of good against the forces of evil in the form of the heretical Safavids. I doubt the propaganda of earlier Islamic realms took on such apocalyptic overtones, but such was the nature of imperial competition in the sixteenth century.

Şahin, Kaya. Empire and Power in the Reign of Süleyman: Narrating the Sixteenth-Century Ottoman World. Cambridge: Cambridge University Press, 2013.