Apologies in advance if I don't use the right terminology here - I'm new!

I have read on various threads that people are ringing AA to get their ticket on the system and then paying elsewhere.

I have 3 questions:

1. Can this be done if your only flights with AA are within the US and between the US and South America?

2. Can this be done if there are other OW airlines such as LAN and Finnair on the itinerary that are not part of the e-ticket brigade?

3. Can it be done with 20 segments on the itinerary?

This is my *ONE5 route:

LHR-PEK,BKK-HKG-PER,SYD-CHC,AKL-LAX-MIA-AUA-MIA-LIM-SCL-CJC-SCL-PUQ,RIO-MIA-CUN-MIA-YUL-LHR

18 segments but could be 20 if I started elsewhere...