Is it possible to survive the Yellowstone Super volcano eruption?

Likely they would not survive due to the extreme temps and volumes of ash unless the shelter was designed to maintain a livable temp and has a self-contained air supply and could withstand the strong earthquakes likely to accompany the eruption. It would be a good idea to do some general research on the extent of previous eruptions (Google Yellowstone hotspot, Yellowstone eruptive center) to get a better idea on what would be expected that close to the caldera. Additionally, the area where your shelter would be would likely be under several tens of meters of superheated ash that would be lethal to enter even after 1 year and likely might be a welded-tuff (a type of volcanic rock) that would entomb your survivors in solid rock. So what I am saying is that it would be very unlikely that they would survive.