In the game 'Pike and Shot', light infantry have the ability to disperse to evade charging cavalry, and then spontaneously reform.
Is there evidence of this occuring in actual battles?
As a general rule, it's wise to be very careful in making inferences about anything based on a videogame. With that in mind, I would say generally, no - "dispersing" would be among the very worst things you could possibly do when faced with a cavalry charge. A charging horse runs around 30-40 miles per hour. That is twice as fast as the fastest humans can run. So out-running a charging horse is not really possible, even if you don't have to worry about heavy armor or equipment.
Furthermore, let's consider the means that infantry have to resist a cavalry charge. Horses, especially trained warhorses, have no problem running down and trampling a man on foot. Some can even be trained to rear and kick or bite an enemy in the face. The famed Lippizanner horses are still trained in many of these maneuvers, even today (except for the biting!).
However, what virtually NO horse will willingly do - indeed, what every horse has an instinctual reaction NOT to do... is to charge headlong into a large body of people where they cannot see the other side of the formation. While I am no horse psychologist, I imagine this invokes a level of fear in a horse which is equivalent to a human running headlong at a brick wall. Infantry commanders have known this since antiquity, resulting in the Square formation, which persisted because of its usefulness until the very end of cavalry tactics. Take a look: https://en.wikipedia.org/wiki/Infantry_square
Therefore, we can say that, by far, the safest thing to do when faced with a cavalry charge is to crowd together in a dense formation. Dispersing would only make it easier for the cavalry to run men down individually, and indeed this was often the goal of the charge - to "break" the formation and get the enemy running in different directions. When in small groups or individually, infantrymen are only so many blades of grass for a well trained cavalry regiment. They can be mowed down at leisure.