I don't know enough about evolutionary biology to have much of an opinion on the issue, except that McKenna's theory is a very entertaining idea!
In his book Food of the Gods, McKenna proposed that the transformation from humans' early ancestors Homo erectus to the species Homo sapiens mainly had to do with the addition of the mushroom Psilocybe cubensis in its diet - an event which according to his theory took place in about 100,000 BC (this is when he believed that the species diverged from the Homo genus). He based his theory on the main effects, or alleged effects, produced by the mushroom. One of the effects that comes about from the ingestion of low doses, which agrees with one of scientist Roland Fischer's findings from the late 1960s-early 1970s, is it significantly improves the visual acuity of humans - so, theoretically, of other human-like mammals too. According to McKenna, this effect would have definitely proven to be of evolutionary advantage to humans' omnivorous hunter-gatherer ancestors that would have stumbled upon it "accidentally"; as it would make it easier for them to hunt.
In higher doses, McKenna claims, the mushroom acts as a sexual stimulator, which would make it even more beneficial evolutionarily, as it would result in more offspring. At even higher doses, the mushroom would have acted to "dissolve boundaries", which would have promoted community-bonding and group sexual activities that would result in a mixing of genes and therefore greater genetic diversity. Generally McKenna believed that the periodic ingestion of the mushroom would have acted to dissolve the ego in humans before it ever got the chance to grow to destructive proportions. In this context, he likened the ego to a cancerous tumor that can grow uncontrollable and become destructive to its host.
The mushroom, according to McKenna, also gave humans their first truly religious experiences and, as he believed, were the basis for the foundation of all subsequent religions to date. For example, he proposed that the biblical Fruit of the Tree of the Knowledge of Good and Evil was actually an entheogenic mushroom. Another factor that McKenna talked about was the mushroom's potency to promote linguistic thinking. This would have promoted vocalisation, which in turn would have acted in cleansing the brain (based on a scientific theory that vibrations from speaking cause the precipitation of impurities from the brain to the cerebrospinal fluid), which would further mutate the brain. All these factors according to McKenna were the most important factors that promoted evolution towards the Homo sapiens species. After this transformation took place, the species would have begun moving out of Africa to populate the rest of the planet. Later on, this theory by McKenna was given the name "The 'Stoned Ape' Theory of Human Evolution".