Can I configure PostgreSQL programmatically to not eliminate stop words in full-text search?

As per your comment on the previous answer, you can easily switch between using no stop words and all stop words. You can acheive this with a custom search configuration:

(1) You can create a custom dictionary without using the stop words file, for example:

CREATE TEXT SEARCH DICTIONARY english_stem_nostop (
    Template = snowball
    , Language = english
);

Note, in the above I left out the StopWords parameter.

(2) Then create a new configuration to use your new dictionary:

CREATE TEXT SEARCH CONFIGURATION public.english_nostop ( COPY = pg_catalog.english );
ALTER TEXT SEARCH CONFIGURATION public.english_nostop
   ALTER MAPPING FOR asciiword, asciihword, hword_asciipart, hword, hword_part, word WITH english_stem_nostop;

(3) Then, when searching specify the config you want use (alternatively you can change the default_text_search_config option each time), eg:

SELECT
    title
FROM
    articles
WHERE
    to_tsvector('english_nostop', COALESCE(title,'') || ' ' || COALESCE(body,''))
    @@ to_tsquery('english_nostop', 'how & to');

You can specify just 'english' in the above SQL to use the normal config.

Note, in this example that using the standard configuration will result in notices because there are only stop words.

Bear in mind the following, however:

• If you are using indexes, you will need two - one for each configuration. (see these docs: tsearch tables and triggers).
• Double check which parser tokens you want to use this mapping as per step #2, above (see Parsers).

No, the stop words are only configurable through that file. You can have a server side function that modifies the file, but that requires the file to be write:able by the postgres service user, which you probably don't want.