Engine start program vehicle will do just that. They will start up and run at idle. They may not go into gear or roll on to a trailer so it's usually the case that they will beed to be winched or forklifted on.
For example, a vehicle can run as part of the engine start program and literally not have wheels. It does start and may even go into Drive. But it will do no good if it cannot role and steer.
Just like the "Run and Drive" listings, Copart does not guarantee a car will be that way by the time auction ends. With Copart, it's always as-is with no guarantees. In our experience however, vehicles listed run and drive or engine start will normally be as described.