You will have to customize full page cache.
Create a simple module.
Create a file called etc/cache.xml
<?xml version="1.0" encoding="UTF-8"?>
<config>
<placeholders>
<fido_example>
<block>block_name/catalog_product_view_addto</block>
<name>product.info.addto</name>
<placeholder>CACHE_TEST</placeholder>
<container>Namespace_ModuleName_Model_Container_Cachetest</container>
<cache_lifetime>86400</cache_lifetime>
</fido_example>
</placeholders>
</config>
Then create a file Model/Container/Cachetest.php
class Namespace_ModuleName_Model_Container_Cachetest extends Enterprise_PageCache_Model_Container_Abstract {
protected function _getCacheId()
{
return 'CACHE_TEST' . $this->_getIdentifier());
}
protected function _getIdentifier()
{
return microtime();
}
protected function _renderBlock()
{
$blockClass = $this->_placeholder->getAttribute('block');
$template = $this->_placeholder->getAttribute('template');
$block = new $blockClass;
$block->setTemplate($template);
return $block->toHtml();
}
protected function _saveCache($data, $id, $tags = array(), $lifetime = null) { return false; }
}
Your Block/Catalog/Product/View/Addto.php
class Namespace_ModuleName_Block_Catalog_Product_View_Addto extends Mage_Catalog_Block_Product_View
{
}
Now, template/layout/your_layout.xml
<catalog_product_view>
<reference name="product.info.addto">
<action method="setTemplate">
<template>your_folder/catalog/product/view/addto.phtml</template>
</action>
<block type="block_name/catalog_product_view_addto" name="product.info.addto.custom" as="addto_custom" template="your_folder/catalog/product/view/addto_custom.phtml"/>
</reference>
</catalog_product_view>
Make duplicate template/catalog/product/view/addto.phtml
file in your template/your_folder/catalog/product/view/addto.phtml
and call this function in that <?php echo $this->getChildHtml('addto_custom');?>
removing everything else.
Then create another file in that folder called addto_custom.phtml
and have all your addto.phtml
content.
Now this should turn off your FPC for addto_custom
block.
[UPDATE]
I had a mistake in extends Catalog_Product_View
section, it should be Mage_Catalog_Block_Product_View
.