Yes and no :P (if that makes any sense).
While the actual game data saves in the cartridge, the Wireless Internet information for that specific game cartridge is stored in the DS (where your access point is, which router you use etc). This isn't the end of the world though. All this means is you'll have to set up your Wireless Internet connection again, which only takes about 2 minutes. (That is, if you even use the Wireless Internet). After that you're good to go!