The answer to that question is always "it depends."
Who actually retained title to the car. If it's the dealer, the answer is yes.
Did Barnes give permission for the tracking, in say, the fine print in the loan agreement. If so, the answer is yes.
If neither of those cases obtain, then if the tracker was placed on the outside of the car, if the tracker was placed there without trespass on the property where the car was pared, and if the tracker relayed no more information that would have been available had the dealer assigned someone to tail Barnes, then the answer is yes.
Otherwise, no.