Oops, I made a typo.

Instead of ".. returns true", I meant "... returns false".

Thank you for taking the time to write to us, but this is not
a bug. Please double-check the documentation available at
http://www.php.net/manual/ and the instructions on how to report
a bug at http://bugs.php.net/how-to-report.php

Actually the problem is that interface ArrayAccess was not designed to support this. In fact it was designed to only check for existance (neither isset nor empty).

Eventually we could change the interface in PHP 6 or invent some workaround for SPL's ArrayObject/ArrayIterator later.

In case you always need empty you can overwrite offsetExists.

Actually, ArrayAccess seems to be able to handle this, the following code will work as expected:
<?php
class demo implements ArrayAccess {
    public $array;
    function __construct()
    {
        $this->array = array('index' => '', 'index2' => 'not empty');
    } 
    function offsetExists($offset)
    {
        if (isset($this->array[$offset])) return true;
        else return false;
    } 

    function offsetGet($offset)
    {
        if ($this->offsetExists($offset)) return $this->array[$offset];
        else return (false);
    } 

    function offsetSet($offset, $value)
    {
        if ($offset) $this->array[$offset] = $value;
        else $this->array[] = $value;
    } 

    function offsetUnset($offset)
    {
        unset ($this->array[$offset]);
    } 
} 

$arrayObject = new demo();
if (empty($arrayObject['index'])) {
    echo '1';
} else {
    echo '0';
} 

if (empty($arrayObject['index2'])) {
    echo '1';
} else {
    echo '0';
} 

?>

Thank you for your bug report. This issue has already been fixed
in the latest released version of PHP, which you can download at 
http://www.php.net/downloads.php

This seems to have been fixed in 5.2.1, so I'm closing this ticket.