How do I search for contacts with "not empty" multiple records field?
In a stock installation of Civi 4.6, I don't think this is possible.  However, this is possible in Civi 4.7: https://issues.civicrm.org/jira/browse/CRM-16137

This is a very simple patch, so if you want this functionality today, check this out: https://github.com/civicrm/civicrm-core/pull/5435/files