Will insurance pay if it is not your fault and you have no insurance?

If "it" is not your fault then you do not have to pay regardless of insurance. However, you may have to prove in court that "it" is not your fault and although you can counter sue to recover your court costs if you win the case, your lawyer will probably want some money up front, and you might lose even if you are not at fault.

As for whether insurance will pay- they only pay for the people they insure subject to the conditions of the policy. If you caused the damage you are likely legally liable even if you did not intend to cause it.