No. Although insurance policies allow insurance companies to control whether to settle cases, there are laws which prevent juries from being told about the insurance available to pay claims. In fact at a trial, the jury can not even be told there is insurance.
Often insurance company lawyers use tactics to try and fool the jurors into believing individual people or businesses who have insurance will be the ones who will have to pay compensation. I know because I was an insurance defense lawyer. Insurance companies use this tactic in hopes a jury will like the defendant and hold back fair compensation. When that happens the insurance company profits, and it costs all of us because we’ll have to pay for medical care and lost income and productivity.