Yes, it is true that all 493 Pokémon have the ability to follow us. So, those who have now gotten to hear and once wondered whether or not the starter will be able to stick behind you even after evolution, it is possible. However, the first Pokémon in line for your team will be the one out of its ball, or so it was told to be.
Though, when you stated that shiny OW sprites have been retained I beg to differ on this right now. For starters, I wouldn't mind getting to know where you learned this information. The reason why is because nothing has been told as yet. Not to forget we've seen the Gizamimi Pichu and Pikachu Colored Pichu with their differentiated sprites so it is a possibility for the shinies. Though, it hasn't been confirmed as yet so I wouldn't say it won't happen and I'm not going to say it will.