maybe...maybe not
The wheel didn't skid. The bike didn't slow. The stick didn't even brake a spoke. I wasn't travelling that fast. My gut feeling is an aluminium or steel frame would have coped with it. Carbon is great if you are sponsored or plan to buy a new bike each year.
Incidentally, in the roadie peleton I train with, in the last 5 years, I have only ever seen one cracked aluminium frame (an ultralight weight Italian frame ridden by a 80kg bloke) while 4 carbon frames have been returned because of cracks.