Yes it will.
A friend of mine has a European DS, and he has the Japanese Nintendogs, Jump! Superstars, and this Japanese Naruto game, and he also plays American and European games on it.
I myself also have a European DS, and I have the US version of Kirby Canvas Curse, but I also play European games on it.
The DS, like the GBA, has no region protection, you can play anything on it that you want.
However, some Japanese titles might not be able to wirelessly interface with say, a US version of the same game.