The short answer is: Usually, yes.
This is because not every contact a person has with the police is a “search and seizure” within the meaning of the Fourth Amendment. The police are free to follow you around anywhere you go if you are in public. They don’t need any level of Reasonable Suspicion or Probable Cause to do this. Thus, an officer may follow a suspect for quite some time and then use his appearance after the stop to establish Probable Cause of a DUI arrest.
But there are some limitations to this rule. In the case of State v. Medlar (1994), a police officer sought to personally hand out a parking citation to a defendant who had parked in an emergency fire lane instead of following the normal practice of just putting the ticket on the windshield underneath the wiper blade.
When the defendant got to his car, the officer sounded an air horn and spotlighted the defendant to get the suspect’s attention, but the defendant thought that this was the work of a prankster (he apparently could not see behind the spotlight) and ignored the officer and drove off.
The police officer pulled defendant over to give him the citation. While doing so, the officer noticed indicia of intoxication and gave the Defendant field sobriety tests, which the Defendant failed. The defendant was arrested and took the test back at the station, which the defendant also failed.
The trial court would not suppress the evidence and convicted the defendant. But the Court of Appeals reversed the conviction because the evidence of the failed sobriety and blood tests violated the Fourth Amendment since the officer had no articulable reason to stop defendant other than to personally give him the parking ticket. The Court of Appeals reasoned that the officer could have issued the ticket while the car was parked and before defendant arrived or drove away. Because of this, the Court of Appeals held that the issuance of a parking ticket was an insufficient reason to stop the defendant. Since the stop was neither investigatory nor supported by articulable facts, the field sobriety and blood tests were in violation of the defendant’s Fourth Amendment rights and had to be suppressed.
But the police can’t act too out of character and beyond the norm in watching you. One Ohio Court of Appeals confronted the situation wherein the officer waited until a parking violator had returned to his vehicle and then after making certain observations, arrested him for DUI. This stop was held unconstitutional.