Does Yosemite Beta update itself to the final version? The title says it all, I think. 
I am installing Yosemite onto a MacPro, and doing it from a Yosemite Beta installer I moved to a thumb drive. It looked like it went well, and it updated itself about 8 times, version 2-6, and then an "OS X Update Combined Version 10.10.5". Does that final update mean I have the full regular install, or is it still a Beta?
No - in general, the builds that are GM Candidates are marked as final and you need to go install the correct update intentionally. Sometimes a 10.x.1 update arrives in time for you to jump on that automatic update, but you should follow the specific directions bases on how you obtained the beta for how to get back on release updates. The steps differ for different programs.