Excluding content from Smart Search when contained in web parts with visibility only to certain role

When setting visibility on an editable text web part such that the web part is only visible to users in certain roles (CMS Editors, for example), is there a way to configure the Smart Search index to exclude this content? What I've seen in v9.x is that the Smart Search indexes and displays content to anonymous users that is inside of editable text web parts whose visibility is restricted to specific roles. I know that page permissions can be checked in the search results web part, but I'm curious if Smart Search is smart enough to be able to not index content in role-restricted web parts. Thanks! Jason