It would hardly be effective at all in a case like the one you described. However, things would be very different if the individual responsible for the hit-and-run offence and the accident were taken to hospital.
If, one hour later, there are reasonable grounds to believe that the individual has been driving under the influence of alcohol during the past three hours, a breathalyzer test would be in order. This information could come from the police officer in charge of investigating the accident, given the fact that a witness has declared that this individual was driving. If both conditions exist, the individual can be required to undergo a breathalyzer test.