If we could green the Sahara, would it be able to sustain itself?
The biggest detriment to keeping deserts green is of course water. With rainfall in the desert limited, afforestation is a tricky and potentially dangerous thing to do. China tried this for decades with afforestation efforts, planting billions of trees in steppe regions of China and Mongolia, only to later worsen because the trees consumed too much ground water and lowered the water table.

On the other hand, trees behave like humidifiers, the little moisture that accumulates at night may collect on the trees and fall as dew, replenishing some soil moisture. Reforestation campaigns in deserts are questionable efforts, without artificial watering or human maintenance they usually die. However active afforestation campaigns in semi-deserts bear some merit. However, there's no evidence of artificially planted forest sustaining itself in such an arid environment without human intervention.
Another example are drought tolerant trees, like acacias, planted in the Sahara. These may very well sustain themselves with their ability to settle and accumulate more water.

They provide shade and so prevent the surface soil from overheating, which has several benefits

With cooler soil, the little soil moisture that falls here can percolate into the ground without evaporating
It shades wildlife from extreme heat (who in turn produce fertilzer i.e. manure/urine)
The areas under trees become attractive nesting sites for birds who nest in winter

For more examples of greened ecosystems, there's the Hawaiian island of Ni'ihau. This is privately owned and very arid because of the rainshadow effect. The owners planted tens of thousands of trees a year for decades. As a result, the trees act as a humidifier to collect what little atmospheric moisture accumulates at night when it's cooler.
Another example is Ascension Island. In the 1850s, botanists (under encouragement by Charles Darwin) started shipping trees to the island. In mere decades, the peak of the island became a cloud forest.
I don't know if such examples are self sustaining. I can only say it's &quot;Plausible&quot;. Ascension Island is not well developed, therefore little maintenance is done on the forest above, and it's a national park.
In more arid regions, it's possible but don't expect a full blown forest. You might see a semi-arid scrub forest.