I would be less worried about bytes and more about the general TCP handshake/acks making it through. You can easily add height, heart rate, and all other kinds of information before you come close to the network overhead. You could also gamble UDP+overhead, but I assume you want some kind of assurance that your SOS made it through.

You also need to be able to get a session within the beam. If you're stuck in the middle of a desert you'll be fine, but if you're within range of a minor town you may not be able to get any signal.