Can driving drunk be considered strict liability?
Depends on which country you live in, but in the United States, driving under the influence is a good example of strict liability prosecutions. It is a case where public safety is threatened, and the government's primary concern is adding deterrent value to the criminal offense of DUI by essentially making convictions easier to obtain.
The main difference with strict liability being that they do not have to prove mens rea, or the presence of a guilty mind (intention to do harm) in order to be convicted. This makes both prosecution and conviction more likely as the only thing that has to be proven in court is the negligence of driving under the influence, as opposed to willful intent to do harm.