[willyg302]

It is completely possible. Consider that the major uses for a server are interacting with clients, storing data (backend database) and manipulating that data. Here the clients can interact directly with S3/Dynamo, this in turn will trigger Lambda functions to manipulate data, and the round trip can be accomplished via SNS.

Of course, it would be much more viable to have some sort of server running (for example I doubt Netflix has replaced their entire backend with Lambda functions), but a great majority of workflows dealing with stateless data manipulation and events can now be streamlined and even replaced.