Is it possible to generate a box-shadow that follows the shape of a clip-path polygon?

You can use a filter on the containing div, try:

.container {
   filter: drop-shadow(0px 10px 5px rgba(0,0,0,0.1))
}

eg: https://plnkr.co/edit/kePuv7OLQwawPjiBLg3J?p=preview