Aaron,
Currently we only offer file upload/download (via FilePublisher/FileSubscriber) but the correct workflow is slightly different than what you describe. If a client is using FileSubscriber to listen to file events it gets notified as soon as the file upload starts, while the file upload is in progress and when the upload is ready. You still cannot get data while the file is being upload but at least you can make the process automatic.
If you need something more real time you may have to implement your own data transfer, by creating a node with items that contain binary data (chunks of your file) and implement your own flow control (if the file is small enough it may be ok for the publisher to publish the full file even if the subscriber is slow in receiving and removing them, if the file starts to get bigger you really want to publish only a few chunks and then wait until they are consumed).
You could implement this also with RTMFP and Stratus if you use the data messaging API (shared objects or NetConnection.call). Those guarantee data integrity, in order to be compatible with RTMFP (RTMFP is a connection oriented protocol on top of UDP, same as TCP but with the ability to drop packets that are "droppable", like video frames and such)