How long's it going to take your to get your IR sorted? If you're just about to start the course and can reasonably expect to have the IR within a month or so, go ahead and get your CV in. If you're not booked to start the course for a good while, then don't waste their time!
Most employers are prepared for a bout a three month lead time in getting new employees. Sure, occasionally opportunities arise for those who can start tomorrow, but they are the exception rather than the rule. I would say it's time to start getting your CV exposed to that big, bad world.
Good luck
Scroggs