No, the template directives in the CMS are not as flexible as the layout XML, the {{block}}
creates a block and renders it immediately, which makes it impossible to create a hierarchy of multiple blocks with it. Also, with the parameters you can set data, but not call methods, so inserting existing blocks as child block is also not possible.
So what can you do instead?
Create a custom block type which creates its own children. If you need to different children in different static blocks, you can control it by parameters.
Example
Blocks
class Stack_Cms_Block_Child extends Mage_Core_Block_Template
{
}
class Stack_Cms_Block_Wrapper extends Mage_Core_Block_Template
{
protected function _construct()
{
if ($this->getData('make_child')) {
$child = $this->getLayout()->createBlock('stack_cms/child');
$child->setData('something', $this->getData('child_something');
$this->append($child);
}
}
}
CMS
{{block type="stack_cms/wrapper" make_child="true" child_something="42"}}