Pipeline trigger job properties get recreated (deleted and re-added) from scratch in each build. This is not ideal and could also cause some trigger downtime, ad there seems to be a period of time where a job could have no trigger at all.
Andrew Bayer just had the time to do some tests. With both. Everytime you execute the pipeline with a trigger, the trigger is stopped and re-started (meaning the Trigger `stop` function is called).