Reddit reviews Snorain Big Box Bay Battle Burst Set, Red 48

Slight error in your math - the Nunchuck™ can catapult nuns up to 15 feet, not 7 meters. Usually when talking about catapulting something, it's already meant distance along the X-axis, not the Y-axis, so it's probably 4.572 meters in distance, not height. So it's 65.6 shots per pellet to reach 300 m, thus 328000 shots, 1312000 seconds or 364.4 hours or 15,2 days of nonstop nun chucking.
Another issue is that we are assuming here an unbreakable Nunchuck™. But I have a nagging suspicion that the spring or the plastic hinge of the Nunchuck™ would give up way before anyone could finish those 328000 chuckings. Thus, since the question posed was "can it chuck?" - a singular Nunchuck™, then my opinion would be - no, it probably can't.

P.S. If you want to have more accurate calculations, then it seems, that the original nuns are 1 inch tall. Source

The best nunchucks I've seen:
http://www.amazon.com/gp/aw/d/B000GKXY34?pc_redir=1411726397&robot_redir=1