I'm assuming that "stream key" was a typo. Do you actually know how to use a steam key? Theres a button bottom left in steam. You dont need to access the shop page to add a game with a key. So bottom left -> Add a game -> Activate a product -> copy paste key here. Done
Either way, since you would have access to the game through ITCH even if you wouldnt be able to use the key you wouldn't really be missing out on anything but being able to launch through steam. But if i had to guess i'd say you're still be able to use the key, just a guess tho.