Hi!
I never tried, but as SpatiaLite uses the SQLite engine it may work.
I checked the SpatiaLite examples and the apps first open the connection to the SQLite database and then loads the SpatiaLite library, so it is easier in this way.
Your application must open the SQLite database using an URI like this one (for a secondary node):
"file:data.db?node=secondary&connect=tcp://<server>:<port>"
And it must check for db_is_ready before executing any SQL command, even SELECT. After it returns true you can load the SpatiaLite library.
Another option is loading the SpatiaLite library as a dynamic extension to SQLite:
SELECT load_extension('spatialite_dynamic_library_name');
Inform me if you succeed. If you encounter any problem, feel comfortable to contact me. Even via e-mail.
Happy testing!