DS Lites are discontinued and most people won't buy them anymore even if they aren't. DSi and 3DS do not have the GBA port. The GBA games also have a battery that will stop all time based events once it runs out.
Since you can go to Kanto in HGSS, you can obtain all Kanto pokemon. The only one left is Hoenn.
From memory, you cannot get all the Kanto Pokemon in HG/SS. Even if you could, your point has already been rendered as moot as you can get all of Hoenn's Pokemon minus Jiranchi and Deoxys between Gens 4 and 5. I believe you can get all of them minus the Starters and the Weather Trio in Generation 5 (still excluding Jiranchi and Deoxys who are Download Events anyway so you can't even get them through main game events)