Can my MacBook Pro be opened by someone else if they have my Magic Mouse 2?

I cannot locate my Apple Magic Mouse 2 that is synced to my MacBook Pro. Can someone else access my computer using that device? The "bluetooth" system preferences last menu option states to allow bluetooth devices to awaken your computer. I unclicked this option just in case.

Also, is there any way to find your Apple mouse if you have your serial number?