Cats can absolutely miss someone like that, and they'll let you know about it.
Our daughter moved out of the house three years ago to go to college, but she comes home for summers and winter break. There's no question that the cat misses her. For the first week or so after she heads back to school, the cat will hang around outside her (closed) bedroom door, even paw at it a few times. After a while, the cat gives up, figuring she's gone for good. Then she'll call from school and we'll chat on speakerphone. The cat will run upstairs and start pawing at her door again, and keep it up for a few days. She knows our daughter is still around, somewhere, she heard her voice! Then our daughter comes home, later heads back to school, the cat hangs around outside her bedroom door for a week, rinse and repeat.