"Complete" generally refers to the school receiving your secondary and informing you that your application is "complete" - at least on SDN. This is the step before it goes "under review" - which is followed by an interview decision (or not).
As to whether the school will send you a secondary, that is specific to the school.
Allow me to clarify.. when I refer to "completion," I am referring to both letters of recommendation and the secondary application itself being processed and "under review."