Programmatically added taxonomy terms not being indexed
You're correct. The core taxonomy module doesn't index or display entities other than nodes. taxonomy_build_node_index() is only for nodes. 

It sounds like the solution you're looking for is Taxonomy Entity Index.


  The Taxonomy Entity Index module maintains a normalized index of all
  terms associated with a specific entity and revision. The core
  {taxonomy_index} table only maintains its data for published nodes.
  This module maintains its data for all entity types (regardless of
  published or not) and also indexed by revision.


It also supports views integration so you should be able to create a view of users who have been tagged with your taxonomy.