Conditions plugin cannot do this and plugin API does not provide a way to turn off required fields check for particular fields in CB. If you really want to do this, you could make a plugin, which would:
-insert some data to required fields before the user profile is created so that CB checks do not fail
-remove this data from the profile immediately after registration
Extended Selects plugin uses something similar to this to go around field value validity check.
This would be an ugly hack though.
-Mikko