---Making limitless possibilities much more limited.
First point: The static stretching usually used by people is scientifically proven to only do damage and weaken your muscles and performance. Please don't encourage your employees to do that.
Having said that your idea is good if you can get people involved. It would provide community building / teamwork benefits as well as health benefits.
Incidentally, there is a lot of research also to prove that exercise and greater fitness improves your energy level - so it is a great enhancer of productivity. An excellent book to read on the subject is "The Power of Full Engagement" by Jim Loehr and Tony Schwartz. I highly recommend it, 5 years ago it transformed my approach to productivity- not just in work, but in life. I've never looked back...
Maximize Health and Fitness with Minimum Time Investment