Short answer : no. Long answer : It wont because the graphical abilities of the 3ds are greatly improved over the original ds. It's similar to the step up from gameboy to gameboy colour. Gameboy colour games will load on the gameboy, but will tell you that, in order to play the game, it must be played on a gameboy colour.
Actually from what I've seen the 3DS games wont even fit into the slot of an older DS because they have an extra little tab on them.