Creating a case-insensitive and accent/diacritics insensitive search on a field

I would like to know if it makes sense to create an index combining two functions while using Full Text Search: lower(name) and f_unaccent(name) Where f_unaccent is just my wrapper to make unaccent function immutable. I do have an index working on: f_unaccent(name) using varchar_pattern_ops. My question is: would an index that combines lower and unaccent functions be triggered by full_text_search lower(f_unaccent(name)). I don't know if the lower function would be useful working with Full Text Search algorithms.