The answer is, probably not. While renters insurance can cover accidental damage, most jurisdictions have laws regulating the use and discharge of firearms. Even though your brother fired the gun accidentally, his actions would still be considered negligent, and therefore the damage would not be covered under his policy.
The likely scenario is that the landlord will fix the wall and then bill your brother for it without filing a lawsuit. In this case, your brother would need to pay out of pocket for the cost of repairing the wall.