Is index on column updated if the column is updated but data does not change?

I have a BEFORE UPDATE trigger on a table that calls the tsvector_update_trigger() built in function to update a tsvector field.
Since this trigger is called for every update to the table, the trigger function will be called even when the tsvector related field is not updated.
My question is, does the index on that tsvector column get updated each time, even though the column is being updated with the same value? If it is I could replace the build in tsvector_update_trigger() function with my own trigger function that does a check before, if not I could just keep things the way they are.
Thanks
riya