Magic 8 ball says "unlikely"...
Size isn't everything. The reason Eyjafjallajokull caused the problems it did is due to the reaction of water with the eruption. More steam/water gives more "ash" (read: Higher explosivity due to mixing) and as such a greater risk to planes. It all depends on the reaction of the water from the glacier.
Depends if it blows fully or just lets of a small effusive eruption. The latter is probably more likely.
As for Yellowstone, even with an eruption rivalling its biggest it wouldn't wipe out mankind. We'd have a lot of rubbish years but we as a species wouldn't become extinct (human ancestors have already lived through multiple eruptions of this size and they are normally not causes of large extinction events.
That's because someone on Horizon couldn't count...
Well probably more to do with trying the scare tactics.