I'm flying the DA42 presently and notice on the online schedule, most all planes and instructors are still booked out at least 5 business days in advance, if not more. And this means being booked solid from 7-8am to 5-7pm pending the instructor. So at least from my view point, things are very busy and would mean instructors are still needed.
Best thing to do though is what Josh said. Call Falcon and ask them directly. I'd imagine the best time to call would be 3-4 weeks out from being able to start a position since anything in the 5+ week range may be too early since needs could change quickly given the state of the industry. But then, things look great at Falcon for the long term since they have substantial international students with a good mix of domestic as well.
Oh, and I plan to be an instructor with them and stick around for a long time since my sights are not on the regional route, it's on the corporate route. They'll have my resume in hand by the end of June or first part of July I believe, if not sooner. Falcon is a great place to instruct from what I seen (that comes from the student perspective of course since I am not an instructor there yet as I'm finishing my CMEL rating up over the next couple weeks).