Is this a work around? If the administrator is logged in all the time, Clients with their correct PW can search their password protected folders?
As the logged in account owner, you can search through all your galleries, including password protected and unlisted galleries.
Visitors to your site can only search public galleries that are not password protected. You can check on that via the gallery settings > security&privacy section. Privacy would need to be set to public and there shouldn't be a password entered.
In addition, the 'hello smuggers' setting in the gallery settings of the gallery would need to be set to 'use site-wide setting' and in your control panel > settings tab you would need to have 'hello smuggers' set to at least 'no - make me an island' for search to work within your site for visitors. Check the SmugIslands help page for additional details.