Yes, that's possible. Safest bet is probably to use a database query in a Query action otherwise looping through the connections API 500 times during every registration would be a bit heavy. The database table for connections is _comprofiler_members. The below is an example of creating a two way connection between a user and all other users.
Code:
INSERT INTO `#__comprofiler_members` ( `referenceid`, `memberid`, `accepted`, `pending`, `membersince` ) SELECT '[user_id]', `id`, 1, 0, NOW() FROM `#__comprofiler` WHERE `id` != '[user_id]';
INSERT INTO `#__comprofiler_members` ( `referenceid`, `memberid`, `accepted`, `pending`, `membersince` ) SELECT `id`, '[user_id]', 1, 0, NOW() FROM `#__comprofiler` WHERE `id` != '[user_id]';
krileon
