Try 

    <?php 
    if ( !empty( array ( $curauth->facebook ) ) || 
         !empty ( array ( $curauth->linkedin ) ) || 
         !empty( array( $curauth->twitter ) ) )
    { 
        echo 'echo me if any $curauth info exists'; 
    } 
    ?>

<sup><b>Note:</b> This can be all on fewer lines, I've just put in additional line-breaks to make it all fit to avoid a horizontal scrollbar.</sup>