Thanks for your question. Since Bluemix is not a required tool for this hackathon extended Bluemix trials are not being provided. That said, you may still sign up for and use a 30-day Bluemix trial if you wish.
It says "Any application that is or was funded or compensated, partially or fully, by IBM for its development is not eligible for entry." so if you are sponsored Bluemix access, you would not be able to submit said app.