Yes, but "the year without a summer" was from one point source, the mount Tambora over a period of about four months on the Southern hemisphere, versus about 40.000 nuclear warheads (wiki gives max 60.000 warheads in 1983) in a few days, on the Nothern Hemisphere.Oh God, yes. It just absolutely goes to complete hell. The level of regression is disturbing, the final scene horrifying.
Edit: The only thing I think about Threads that is unrealistic is that the nuclear winter effect is overblown. 25°C temperature drop in summer seems ridiculous. That would mean temps as low as 23°F/-4°C in June/July. I feel like that strains credulity, since even "The Year without A Summer" in 1816 saw only a 3-5°C drop.