Maybe. In most insurance policies there is a provision that excludes coverage for an intentional act. However, in New York, if the bodily injuries were unexpected, unintended, negligent, reckless or unforeseen, the insurance coverage may apply and would be liable to pay for the injuries caused by the defendant.
As an example of a case in New York, a college student jokingly pushed a 55-gallon drum from a window of a fraternity house that struck another student. The insurance carrier provided coverage because the student who pushed the drum out of the window did not expect that the drum would strike someone.