Faceted search using fields from a related node, is it possible?
At the bottom of the fields page you can see additional fields. This allows you to join nodes via relationships.

Search API > Default index > Fields > [Scroll to bottom} > Add related fields


Select your field that is an entity reference.
You'll have access to the fields of the reference too. 
Then select the fields on the referenced node that you need and save.
And return to facets.


http://example.com/admin/config/search/search_api/index/default_node_index/fields#edit-additional