Can a AWS PostgresSQL RDS instance be provided with a stop words file?
PostgreSQL 10

It does just that, you can see the code here,

void
readstoplist(const char *fname, StopList *s, char *(*wordop) (const char *))
{
    char      **stop = NULL;

    s-&gt;len = 0;
    if (fname &amp;&amp; *fname)
    {
        char       *filename = get_tsearch_config_filename(fname, "stop");
        tsearch_readline_state trst;
        char       *line;
        int         reallen = 0;


**stop could be modified easily to read from the yet-nonexistant parameters, but currently it just pulls from the file. A few lines above and you'll find get_tsearch_config_filename(fname,extension) which looks in just the place you were referring too,

snprintf(result, MAXPGPATH, "%s/tsearch_data/%s.%s",
         sharepath, basename, extension);


There is nothing else in the code base that writes to a StopList pointer. As of PostgreSQL 10, it's not possible.

Amazon RDS

There is an unresolved issue from 2014 on AWS Developer for this,

Amazon confirms we're right in saying there is no way


  Unfortunately, because RDS doesn't provide filesystem access, you won't be able to upload your custom files to $SHAREDIR.


And Amazon follows up with


  I have raised a feature request with the RDS team.