Not quite. Gold and Silver have quite a bit of space left; the game is occupied with lots of leftover data (beta maps, for instance). Additionally, Pokémon Crystal's circuit board had a ROM capable of holding more than Gold/Silver, and accommodating the features the game introduced wouldn't take up a significant amount of space either.
It's being pointed out that some parts of the game are narrower than they originally were, mind you. It'd be incorrect to pin the blame on space issues for this game either; DS cards can have circuit boards with a very large ROM size. In fact, commonly we're looking at 256 MB ROMs on most games, which generally include lots of 3D models (of characters). The Pokémon series make sporadic use of 3D (and the mapping is done in a simple way) so I don't see GameFreak having issues with size, even with 128 MB circuit board ROMs (which GameFreak, but not Nintendo of America, use for the Pokémon games at the moment).
Sorry, had to get really technical there. :P