Is it possible for EpiServer FIND to only index Documents that have been added to Published Composer elements?
I know that FIND can index the File Manager but the search brings back ALL items, most of which are not published on the site.
I don't think you can set up this kind of restriction. However you could try setting a client convention to restrict the path in which files are indexed. This would be a convention where Composer uploaded files should be stored, for example a new ~/Composer/ starting point.
You would have a convention like the following:
.ShouldIndex(x => x.VirtualPath.StartsWith("Composer"));