If the immune system is dysfunctional, it will not make antibodies. It's possible to have a very severe infection and no antibodies to it whatsoever. Or one could have antibodies even though the infection has been eliminated.
A scraping of the white tongue and examination under the microscope might be a better test. Moreover, if a lab get get the tongue scraping to grow on fungal culture media, the species and drug susceptibility can be ascertained.