Yes, you should make a claim against the driver regardless of the outcome of their criminal case. Talented criminal defense lawyers can get their clients to avoid a conviction in a variety of ways, often due to police report errors or issues with a breathalyzer test. But a criminal conviction, while it will help your case, has no direct bearing on your civil case. The criminal and civil court processes are different in several ways:
The burden of proof in criminal cases is "beyond a reasonable doubt," but in a civil case it is called a preponderance of the evidence, which is much lower. That means you and your drunk driving accident lawyers will only have to prove it is more likely than not that the driver was drunk and caused your injuries, meaning a mistake in police reporting might not kill your case.
In a criminal case the state brings charges in order to punish the drunk driver, deter others from similar behavior and keep dangerous drivers off the roads. In a civil case, you are making a claim against the driver in order to receive compensation for your injuries and be made whole again.
While criminal courts may sometimes require a drunk driver to pay you some money after a guilty verdict, you will need to file a civil claim with a skilled drunk driving accident lawyer to receive compensation for all of your damages.