It may affect global warming; I doubt it will be much however. It is all tectonics and part of the Pacific's Ring of Fire. Maybe if Yellowstone blew up global warming would be stopped.
I suspect it may be due to a hot spot similar to what caused the Hawaiian islands, rather than a tectonic spreading or subduction. Numerous chains of hot spots can be seen in the South Pacific if you look at a map of undersea stratigraphy. Or not. See section 3 on Island Origins
If Jellystone blows up about ten million people will no longer care.