You could use a custom Textformatter module for this. I quickly hacked together this one, nothing perfect as it replaces all occurrences of opening p tags, but you could spice it up using regex etc. I gave it a quick test – it does it's job. This should get you started:
<?php
class TextformatterAutoClass extends Textformatter{
public static function getModuleInfo() {
return array(
'title' => 'AutoClass Textformatter',
'version' => 100,
'summary' => "Adds a class to the automatic p wraptag of CKEditor" ,
'author' => 'Johannes Dachsel'
);
}
public function formatValue(Page $page, Field $field, &$str) {
$str = str_replace("<p>", "<p class='summary'>", $str);
return;
}
}