Very unlikely, especially as the major industrial nations will come nowhere near to meeting their greenhouse gases emission targets. Major volcanic eruptions, like major earthquakes, are random and unpredictable. The last really big volcanic eruption we had was Tambora, on the Indonesian island of Sumbawa in 1815. That caused climate cooling for a few years, but it didn't cause a mini ice age. It may have helped the Little Ice Age which was already in progress, to last until the middle of the century, but that's all.
Tambora was the biggest eruption in recorded history, dwarfing Pinatubo, Krakatoa and Thera (Thera erupted in the Med near Crete 3.5 thousand years ago and destroyed the Minoan civilisation), so an eruption big enough to cause another Little Ice Age would probably need to be as large as the Toba eruption of about 75,000 years ago on the Indonesian island of Sumatra. The chances of such an eruption within the next 20 years are virtually nil. The Little Ice Age, which lasted about 400 years and ended about 1850, is not believed to have been caused by volcanic eruptions, though such eruptions may have from time to time intensified it and prolonged it.
There is no way of inducing major eruptions short of detonating 50 megaton hydrogen bombs in sites known to be volcanically unstable, but that would not only violate international treaties about nuclear explosions in the atmosphere but would in any case be unacceptable. Fifty megatons is the world record for thermonuclear explosions, by the way, held by the Russians.