All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is no compulsion on embracing Islam in the narrative you mentioned in the Question – if it is authentic. Abu Sufyan fought against Islam and the Muslims, and he deserved punishment for his acts –both based on reason and Islamically. Al-‘Abbaas informed him that if he embraces Islam, he safeguards himself from being killed –a matter which he deserved because of him fighting and killing the Muslims. It is very clear that the statement of Al-‘Abbaas is not a coercion on Abu Sufyan to embrace Islam.
On the other hand, logical and Islamic benefits are apparent in the threat of Al-‘Abbaas to Abu Sufyan, as he was the leader of the polytheists in the war against the Prophet for many years. Therefore, if Abu Sufyan was left alone, it would not have been safe that he would prepare an army from the Quraysh to fight the Muslims again. Was there any war in history whereby the commander of the enemy was set free?
For more details on this story, please refer to Al-Manhaj Al-Haraki lis-Seerah An-Nabawiyyah by Muneer Al-Ghadhbaan, and Fiqh As-Seerah An-Nabawiyyah, by Al-Booti.
Nonetheless, regardless of whether or not this narrative is authentic, Abu Sufyan ibn Harb accepted Islam in the year of the conquest of Makkah, and he was among those who have been recently reconciled to Islam. They embraced Islam either because of fearing to be killed, or because of fearing to be imprisoned, or because of desiring money and so on. Nevertheless, after that, most of them became good Muslims and had correct faith.
Ibn Taymiyyah said: “Most of those who were set free among the prisoners were those whose hearts have been recently reconciled to Islam, and most of them became good Muslims. A man amongst them would embrace Islam at the beginning of the day to gain something from this worldly life, but by the end of the day, Islam would become more beloved for him than all the sun has risen upon.” [End of quote]
There is no doubt that Abu Sufyan became a good Muslim and he fought for the Sake of Allah, and his virtues became famous; no one would deny his excellence and virtue except an arrogant innovator.
Allah knows best.