GitHub pages is only for static pages. So no PHP support on there at all. Jekyll takes markdown and templates and generates static html pages, the result is not dynamic at all.
Grav is not a static file generator, its a flat-file CMS that needs PHP to run. Therefore it won’t run on GitHub pages.
However, there is a possibility that Grav could get a ‘generator’ mode in the future, although it would mean the resulting site is pretty limited compared to the dynamic capabilities it has now (live data integration, search, filtering, ajax, etc)