Maybe. The source material isn't exactly clear.
You can be organized and have a light infantry force, of course. Regardless of how much of the rebellion was based on slaves or not, the Zanj mostly carried out guerrilla raids - which makes one think they had more light infantry than heavy infantry.
One might hypothesize that without the death or apparent death of the leader, the routs would not have occurred, and the charges would not have achieved much.
Huh, somebody who read the original post? Horse archers may also be well-armored, but their main weapon isn't the charge.
At Tours (732), heavy cavalry broke through heavy infantry, but this was well trained, disciplined and well equipped, and the cavalry did not push them into a rout - the smaller army, having no cavalry, won the day.
At Legnano (1176, just to pick something centuries later) the better trained German heavy cavalry easily defeated the Communal cavalry - and then was stymied all day long by a porcupine of heavy infantry, and lost the battle.
Not always, but often, when you read about a successful heavy cavalry charge, you'll have plenty of details about that, and then, some sort of footnote: oh, and the charge was prepared by light infantry/archers/horse archers peppering the enemy with missile weapons. And weakening and demoralizing them, of course. Adn the presence of heavy cavalry had forced them to bunch up, so as to become a perfect target for volley arrow fire. Combined arms, in other words, not just knights in shining armor.
1. I doubt anyone will say that heavy cavalry alone wins every battle per se, even if such may be possible in some scenario. So, the idea that, the army peppers the enemy with arrows prior to a cavalry charge that routs the enemy, is not an argument against the effectiveness of the heavy cavalry. All types of soldiers in pitched battles are tools to be used and utilized for the victory, we might say. But for a victory to be most assured, I would prefer to rely upon heavy cavalry in pitched battles than upon heavy infantry, light infantry or archers, if I had to rely upon any single grouping.
2. All military actions are primarily guerrilla raids and such-- or as we say logistical maneuvers. For instance in most military campaigns, much time is spent besieging towns, raiding villages, besieging cities, negotiating with locals, striking supply zones, etc etc etc... The Zanj had a, according to easily accessed materials on the topic, a rigid command structure to its military forces, with many different localized commanders, lieutenants, generals and marshals. Their plans, as al-Tabari noted, were to both rule the region of Iraq and to raid and pillage Abbasid held lands and strike at the sections that would most limit the Abbasid capability to wage war. This included attempts by the Zanj to cut supply lines to Baghdad from both the east and west, invasions of Arabia and Iran, campaigns in the north to devastate local countryside and using infiltration among its contacts in Karbala to cause mischief for the Abbasid caliphate among the already agitated Shi'a communities. The Zanj further, held their own wide supply lines, began taking taxes, implementing trade laws, protecting communities, minting coins and many other points. Do not continue this line that the Zanj were just some sort of Spartacus rebellion or some type of insurgency like its northern neighbor, the general Khawarij rebellion among the Kurds north of Samarra. Rather, they were creating a counter state-Imamate that under the genius of their leader, used a myriad of different classes and people: slaves, Shi'a radicals associated to the Shumaytiyya, freed criminals, bandits-robbers-pirates, bedouin who resented the Mihna and the Abbasid centralization attempts, Arab tribes who wished to make gains against other tribes in the region who were deprived of their lands (there was according to al-Tabari, an ongoing tribal warfare between different Arab tribes in the vicinity of Basra at the time of the Zanj rebellion, accoridng thus to al-Tabari and Ma'sudi, the Zanj leader infiltrated this conflict with some of his spies in 868 and began directing the conflict towards his gains and aligned heavily to factions that supported his rule), Khawarij revolutionary, generally dissatisfied peasantry and the leader's hardened partisans who formed his vanguard of varied military leaders, government officials and so forth. As I said earlier, one can derive this solely from the major works on the topic, which al-Tabari claimed to be a brief summary of the Zanj state and the Zanj war, while he mentioned a book written at his time that was focused solely upon this topic, that has been missing since 1258 (this book was written by one of the scholars who served the Zanj state and was captured by al-Muwaffaq in the 882 thrust and pledged his allegiance to the Abbasid state, thus he knew more intimately than anyone the situation of Zanj governance).
3. If deaths had not occurred. This is like saying, if the heavy cavalry was not present to perform such a critical strike, the battle would not have been won. It makes one wonder, no?