Legal Question in Construction Law in California

No, it is not negligence to perform unlicensed work. That is an intentional act.

Are you asking about claims against an insurer? A bond? Or claims in a lawsuit?

I we re-worded the last sentence of your question to read, "If I also have property damage from the unlicensed work, can I also make a claim for negligence?" I think the answer is yes. Whether the claim will result in a payment or a judgment will depend on other facts. You may be more likely to prevail in court than in presenting such a claim to an insurer or bondsman.