It will build up the interior sufficiently enough to resist slavers from the coast and thus stop the depopulating mass enslavement of the latter centuries. Nations do not naturally enslave their own citizens and many African polities were destroyed because they refuse to trade their own. What this alternate trade network does is giving inner Africa access to the outside world and speed up consolidation into Kingdoms/confederations etc... It wouldn't stop slavery but it's effects on Africa can be dampened.
When you say slavers from the coasts, are you referring to coastal states in Africa, or European slavers operating on the coast?
Here is the scenario in which I find a dampening of the slave trade in this timeline to be the most likely: A large state, like Mali, controls most or all of the territory that would be home to good sources of slaves for Atlantic trade. Because of this, the African slave traders, whether they be under Malian rule or not, have little supply. An unintended consequence of this would be to raise the value of slaves to whatever the maximum the market could possibly bear.
However, if Mali does not directly control enough of such territory, then being powerful and sophisticated could actually operate in the opposite direction: as a powerful middleman in the slave trade. It could profit mightily by enslaving the people of neighboring states. And if it is more connected overall with the world trade networks - and internal African trade networks, this will likely increase the volume of the slave trade. In this scenario, the only reason I could see it dampening the slave trade would be as a trade tactic, to limit supply to maintain high prices (ultimately the same result as the scenario I propose in the preceding paragraph).
Whether the slaves are being shipped around on Roman, Malian, or other European ships, I don’t think the overall complexion of the trade will change much.