Will extinct volcanoes on the East Coast of the U.S. erupt again?

No. Through plate tectonics, the eastern U.S. has been isolated from the global tectonic features, tectonic plate boundaries and hot spots in the mantle, that cause volcanic activity. So, new volcanic activity is not possible now or in the near future. If you wait around several hundred million years, maybe...

Remnants of past volcanism are found in most areas of the earth, even where volcanoes have not erupted in hundreds of millions of years. They are very common.