In most criminal cases of drunk driving the judge will order some form of restitution. This is typically for out of pocket expenses that have not been reimbursed by insurance. When this is done it does not mean that the victim can’t bring a civil claim against the drunk driver.
The civil case against a drunk driver is looking for pain, suffering, disability, the loss of the enjoyment of life and things like that. This is much different than an order for restitution that was given in the criminal case. The only restriction would be that if the judge ordered the defendant to pay $1000 for a medical bill and they actually paid it. The victim could not then request and receive the same money for the same bill for the civil case. But otherwise it does not limit the ability to bring a civil case because there’s been a restitution order in the criminal case.