Hi Kris,
Yes, adding a background video as such is possible, and here are two articles for assistance with regards to it:
https://docs.generatepress.com/article/background-video/
https://docs.generatepress.com/article/page-hero-background-video/
Either of these should work but you’ll need to have a Header Element with a merge setting to make the header merge with the “Page Hero”.
I would personally prefer using a Block Element – Page here, with a Header Element just with the merge setting for ease of styling.
You can set the Parent Container to 100vh
min height in it Block settings to make sure that it occupies the full height of the viewport all the time.
Example: https://share.getcloudapp.com/Qwunl2AR
Hope this clarifies!