More or less, yes. Proper SABRE integration came last year, and only for businesses.
https://skift.com/2021/08/06/southwests-expanded-partnership...
Looks like Apollo and Amadeus came in 2020.
https://skift.com/2020/05/19/southwest-airlines-expands-corp...
https://www.businesstravelnews.com/Distribution/Southwest-Go...
So if you use "Kayak for Business" you can book Southwest, otherwise you can click through on the ads that Southwest runs on Kayak. And, yes, it was a deliberate (Herb) choice. So was not being an IATA member and not participating in the IATA clearinghouse. The upside is less overhead the downside is less resiliency. You don't need to care about these things so much when you're flying a regional jet on mostly intra-Texas routes out of an airport that only allows short flights. With a fleet of full-sized airliners, "focus cities" across the country, and an international route network things look a lot different.
https://www.iata.org/en/about/members/airline-list/?search=W...