Embedded Video Update - does this reflect in published course

I have embedded a series of videos in my course that are editable at the source. If I edit and re-publish my video I can see the updates are reflected in Rise and in my Share links, but would they be reflected in my LMS or Web published course? Or does that somehow only reflect the version of the video that existed at publish?

We've only hosted our courses as links to date and are looking at options for more trackable content but wanted to know this as it would impact of development pipeline.