Hi,
sorry for late reply, it's a weekedn 
 
 
This seems possible but I does not know how the other component save informations.
Anyway to make this you can build a simple plugin, follow these steps:
- Download, Install and Enable Skeleton Plugin (you will find it at 
http://docs.easy-profile.com/index.php/article/triggers)
- Open file /plugins/jsn/skeleton/skeleton.php
- remove samples functions: triggerFieldAvatarUpdate, triggerProfileUpdate
- add function like this:
public function triggerProfileUpdate($user,&$data,$changed,$isNew){ 
    $alias_of_checkbox = 'HERE_THE_ALIAS';
    $values = (array) json_decode($data[$alias_of_checkbox]);
    // the $values var will contain a PHP array with values of the checkbox:
    $db = JFactory::getDbo();
    foreach($values as $value) {
        // Query for each value
        $query = '....';
        $db->setQuery($query)->execute();
    }    
}
 This code will be triggered when user update own profile.
NOTE: 
This code is not tested and not supported, this is only for example purpose. You need to have a minimum of PHP knowledges