Unfortunately, No. The reason is because Victini, Zacian, Zamazenta, Eternatus, Kubfu/Urishifu, Clayrex, Glastrier, Spectrier, and all three Galarian variants of the Legendary Bird trio are shiny locked, resulting in not being able to get them as shinies. And with that logic, you cannot get a complete Shiny National Pokédex in Pokémon home.
Hope I helped!
Edit: Zacian and Zamazenta are now obtainable as shinies due to an event.