They have nothing on a device that never attempts to connect. The phones are just looking at broadcast send from routers when they are searching the phones are not actively sending anything.
Once a device attempts to connect you might get something but most routers only show what is actively connected there is not a lot of memory to store historic data. Some routers do have a ability to send log messages to a remote server for storage. Still I am not real sure if a device attempts to connect and fails because it does not have the proper key even a router that has logging will track that. I suppose it could but it is not your common router you will find in walmart.