This is an interesting question. Cat owners will have to rely on their own experiences and their knowledge of cat behaviour to answer it because you won’t find the answer in books.
The answer is in human body language and how cat’s observe it. Cats do understand the tone of our voice, its general sound and our body language. They are good observers and can connect our behaviour with the signals we give using the sound of our voice, body language and general demeanour. And a cat can learn from their owner the message that the owner wishes to communicate at a fairly simplistic level. In other words cats can be trained with patience.
“Most cats are extraordinarily sensitive to human body language” – Dr Bradshaw of Cat Sense.
Cats connect the time of day and tone of voice to know when she’ll receive food, for instance. That’s a good moment for the cat. If a person smiles at the same time a cat might be able to connect that aspect of body language with a time when she is fed. Cats don’t automatically understand the human smile as a friendly expression but a cat should be able to learn that the human smile is a friendly signal and perhaps that something nice is about to happen.
Humans inherit or learn the ability to understand the smile but cats don’t. Cats inherit or learn the ability to read cat body language such as the tail up position (signifying a friendly cat) and the nose touch (a friendly greeting). The cat signals friendliness to other cats through the purr as well as it reduces the likelihood of an attack and is a signal of appeasement. So cats are alert to body language signals.
But the human smile is not in their repertoire of expressions although I believe its connection with human actions could be learned. There will be no certainties and it will depend on the cat and the cat caretaker. My theory is based on the fact that cats don’t smile or frown unless the cat is Grumpy Cat – but her frown is an anatomical defect not a facial expression indicating an emotion – and that cats can be trained.
Note: I am guessing to a certain extent and have some doubts whether a cat could recognise the smile but I believe that they can. As for understanding the human that’s a different matter. For cats, as mentioned, it will be more a matter of connecting body language with action rather than a natural ability to understand that a smile means friendliness and happiness (or pretending to be happy 😉 )