There doesn't seem to be much in the way of technical documentation for BMD StagePlayer available.
Eos has many ways to remotely trigger something. Trouble is, there's no way to know whether StagePlayer supports any of them. All I can find is that it's an iPad app, but no details on whether it streams from an iPad or if that's hopefully just a remote interface.
Their website isn't going live for
another week so the question may be a
bit premature.