Would hook_access() hide content from Views/Solr if returning FALSE? If I were to setup my own hook_access() and return FALSE based on a few different criteria, would this then hide the content from a view in modules like Views and Apache Solr?
hook_access() is only called when viewing/editing a single node. For all listings, both in core and views, you need to use the node access system. You also need to use that for node types which are not owned by your module.