Can a cell not talk back to the kernel, who, in turn, should have access to the tornado request data, such as Remote Address, User-Agent?
I'm not exactly sure what you mean by the cell talking to the kernel. The code inside a cell is run by the kernel. The Javascript cell object has a reference to the kernel which it can use for communication.
However, the kernel does not handle HTTP requests. The browser and Javascript talks over HTTP to the notebook server (which is written with tornado). The server communicates with the kernel over ZMQ sockets, so the kernel does not have information about the browser's IP address.