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That is not correct. When AMCAS receives both an application and all transcripts it begins processing (ie enter verification queue). In doing so, it opens a file with your AMCAS ID and "alerts" all schools that you have applied to from this person at this contact info now has an opened file. Some schools will at that point, prior to verification and prior to application transmission, will start sending secondaries. Therefore, you could get, complete, and submit a secondary prior to your primary ever being transmitted to the school. However, secondaries timelines can vary widely as to when to they are sent out from almost immediately upon submissions to 3 months, though most are in the range 1-3 weeks after transmission.
Really? that's pretty cool. Why don't more schools take advantage of that? It would move timelines forward and give them more time to review secondaries.