Is it safe to use a potato salad recipe with cooked potatoes celery onion topped vinegar and olive oil be marinated for several days unrefrigerated before serving?

No, potato salad left unrefrigerated contains perishable items and potentially harmful bacteria can quickly multiply at warm temperatures.

Potato salad must be refrigerated or kept on ice or in a cooler with ice if kept outdoors during a picnic or outing to prevent foodborne illnesses.