Does sleep affect character?
If by character, you mean someone's personality, then sleep certainly plays a big role!
Not only does a lack of sleep make people more fatigued during the daytime, it can have major effects on a person's cognition and behavior. Sleep deprivation can cause depression, agitation, anxiety, poor concentration, forgetfulness, and poor coordination. One night of poor sleep is more likely to have effect on a person's mood, making them more irritable or perhaps distanced from their surroundings. Ongoing, chronic sleep deprivation can have more severe effects, even causing hallucination.
In this way, someone who is well-rested is more likely to "feel like themselves," able to participate fully in activities and interact with others with little to no difficulty. People who are chronically sleep deprived may develop a personality characterized by their lack of sleep-- do you know anyone who is always irritable, forgetful, and tired? Think about the ways in which you feel differently after a good night's rest or a night of no sleep. Giving our bodies and minds that time to process and refresh has a huge impact on how we act the next day!