It does proc a new stack of Monkey's Agility. However, the base cooldown of 6 seconds on all the stances. One stack of MA lasts for about 3 to 4 seconds (I'm unsure of the actual number). Thus, unless you've got some crazy cooldown reduction, it is impossible right now to maintain more than a single stack of MA using a single stance. That's why stance-dancing/twisting (whichever term you prefer) really beefs up Udyr's damage.

What Fuzz said, the cooldown on the skills is higher than what Monkey's Agility lasts for.