I believe I know what your asking(tell me if I'm wrong) but I think your asking if you can keep all your Pokémon if you put your games in the 3DS. Well, you can keep all your Pokémon, but at the moment you can't transfer it to Pokémon y. As you might have read on the home page, PokéBank crashed, so only a few Japanese people have it. As for you data, only transfer it if you think you should, but I'm pretty sure those games save on cartridge. Yes you can still transfer from HG to black 2 and white, no matter what kind of DS you have. To transfer to y, we have to wait for the PokéBank.
PS just to clarify: YOU CAN TRANSFER POKEMON TO ANY GAME EXCEPT Y AND X WITH ANY DS SYSTEM!SOURCE:EXPERIENCE!
PokéBank has crashed, so it's currently in maintenance; Also, you'd have to do it on the 3ds,but you can't. Until it comes out again, you don't have access to Pokebank.If it comes out again, you'd have to buy it in the eshop in the 3ds. If the Pokebank is like past transferring methods, all you'd have to do is got to ds download play in your DSi (with your game in it) and on your 3ds, start the app transfer option.
Hope I helped.