Can I trade pokemon that aren't on the diamond pokedex without the national pokedex?

I wanna start my Diamond game all over again. What I wanna do is after I get my first gym badge and open up trading, I want my friend to trade me a baby Vulpix and Snorunt. They both are not on the Diamond Pokedex... they are on the National Pokedex... can I still trade them to my game without having the National Pokedex?|||Yes you can. The Vulpix or any other pokemon won't appear in your Diamond PokeDex. However, when you obtain the National PokeDex, the Vulpix or any other non-Diamond Pokedex pokemon you obtained will appear in National PokeDex.|||YER OF COURSE! I STARTED WITH CHARMANDER,BULBASAUR,SQUIRTLE,DRATINI in platinum.|||yes you can and when you get the national pokedex the pokemon will be on it.|||Yes, they just don't appear on the PokeDex.|||come on someone need to know this