Maybe, but we need to find a short term usage for them to get this started. Horses were only breed to be stronger and so forth after they already had developed some use. They were not first domesticated with the understanding that they would be used as indomitable war steads, at least that is my assumption.
Meat, feathers, leather, and eggs seem to be the primary reason to manage ostriches today. All of which would be a factor thousands of years ago as well. Indeed ostriches were hunted specifically for all of those things, even their eggshells were used widely as far away as some parts of Europe.
So that would be the start, keep the ostriches for their feathers and eggs as trade goods or for local use, and when the die or are killed their remains could be used for clothing, crafts, or even some kinds of tools like bone needles for example.
From there larger ostriches are selected for, more meat, more feathers, even larger eggs, or more eggs.
With larger ostriches the possibility of riding or using them to pull carts comes into play, making them a valuable beast of burden, especially in more arid areas where ostriches naturally thrive, and other livestock could struggle.
I'm not suggesting that they could really outcompete horses in say North Africa or Arabia or other areas, but they could be a viable local alternative in much of sub saharan Africa.