You can add date of birth to the search form, however, if you try simply searching by year the search is returned empty

C4::Utils::DataTables::Members->Search

 66     if ( $searchfieldstype eq 'dateofbirth' ) {
 67         # Return an empty list if the date of birth is not correctly formatted
 68         $searchmember = eval { output_pref( { str => $searchmember, dateformat => 'iso', dateonly => 1 } ); };
 69         if ( $@ or not $searchmember ) {
 70             return {
 71                 iTotalRecords        => $iTotalRecords,
 72                 iTotalDisplayRecords => 0,
 73                 patrons              => [],
 74             };
 75         }
 76     }