If you've started an application process on the website and they do decide to close applications early, then you'll get an email notifying you. You'll effectively have 48 hours to finish the application. It was open for a good few weeks last time round.
Mike91 - You'll need to bring physical proof of either SQA results or Degree with you to assessment centre if you do get through the papersift anyway. It'll cost you £200 to even get there, so make sure you've found out first. I think unfortunately you'll most likely have to wait until the next FPP to apply as you won't have the necessary document this time round when it comes to proving qualifications. Use the time wisely!