If you are hit by a truck driver with previous drug or alcohol related convictions, it could absolutely affect your truck wreck case against the company who employed that driver. It can demonstrate negligence on many levels such as hiring, supervision, retention, training, and more. When a trucking company knowingly (or accidentally) hires drivers with past drug and alcohol problems, they are shirking a greater responsibility to ensure their trucks are operated safely on public roads.
So yes, a truck driver’s history with drugs or alcohol would likely be considered by a jury when they deliberate on your truck wreck case. Many large settlements or jury verdicts result in strong recoveries for truck wreck injury plaintiffs because of the irresponsible conduct of the company employing the driver, and not just the negligence of the intoxicated driver.