100% chance it WILL happen, it's just a matter of time. It's likely that it would give off some pretty clear early warning signs before it erupts, usually volcanoes will give clear indication before they blow their top. Chances are that people are gonna know about it before it pops.
The ground in Yellowstone is subsiding which indicates that the magma chamber is either cooling and shrinking or magma is somehow finding a way outside of the chamber and into someplace else underground. Both scenarios have upsides and downsides regarding a possible eruption. If the magma chamber is cooling and solidifying that would mean lower overall activity, but it would also destabilize the surface. Generally, that's considered a bad thing. If the magma has infiltrated into some new area and formed a Dike, Sill, or just expanded the chamber that would cause the subsidence but could also lead to the magma finding a weaker spot in the crust to break through. Geologists don't like to make specific predictions because the number of unknown factors in something like a volcano eruption or earthquake is absurd.
The earth will cool because of the ash in the atmosphere and life will be changed for everyone all over the globe, but we'll probably live.
>>11576527California has the San Andrea's Fault. I'll keep doomsday preaching until it happens and then I'll laugh and say "I told you so". It's like a rubber band. If you continually stretch the band, it'll eventually snap. You don't know when or where on the band it'll snap but you know it will.