Not necessarily. There are 2 license suspensions for a DUI - an administrative suspension if there was a blow of .08 or higher or a refusal; and a court suspension upon conviction. If the case went to court, and you were convicted, a suspension took affect at the time of conviction, and you have a conviction and criminal record. If your court case is still pending and the suspension is an administrative DMV suspension, then the conviction by the court has not occurred yet.
If you were convicted of a DUI, you have a criminal record whether or not your license was suspended.