No it isnt the biggest, and no, we all wouldnt die. Those who are left might kill each other off in a war though. So you could be close to being right on that one.
Worlds Largest Supervolcano Is Even Bigger Than Previously Thought (Yellowstone)
Late Pleostocene Human Population Bottlenecks. . . (Toba)
"The last glacial period was preceded by 1000 years of the coldest temperatures of the Late Pleistocene, apparently caused by the eruption of the Mount Toba volcano. The six year long volcanic winter and 1000-year-long instant Ice Age that followed Mount Toba's eruption may have decimated Modern Man's entire population. Genetic evidence suggests that Human population size fell to about 10,000 adults between 50 and 100 thousand years ago. The survivors from this global catastrophy would have found refuge in isolated tropical pockets, mainly in Equatorial Africa. Populations living in Europe and northern China would have been completely eliminated by the reduction of the summer temperatures by as much as 12 degrees centigrade"
Yellowstone is much larger than Toba.