There's nothing really available to create a connection between everyone on the site all at once. You could try doing it with CB Auto Actions in a query action or using the Connections action (can only connect 1 user at a time). Probably going to need a custom solution to loop through the existing users and run though connection API for each one. As for the query usage the below should work (not tested).
Code:
INSERT INTO `#__comprofiler_members` VALUES ( `referenceid`, `memberid`, `accepted`, `pending`, `membersince` ) SELECT '[user_id]', `id`, 1, 0, NOW() FROM `#__users` WHERE `id` != '[user_id]'
krileon
