Edit: Sorry, seems I misunderstood the question.|
No, the copy of the game is recorded as having been downloaded by your console and is preinstalled on it. There's no code, or card, so you can't trade it with anyone (other than via a rather tortuous system transfer which would wipe their machine). If you uninstall it, you can redownload it at any time (until Nintendo turns off the servers) provided you don't change consoles, or at least do a system transfer if you do upgrade to some future 3DS lite.
Edited by mal at 19:01:13 22-04-2013
Cubby didn't know how to turn off sigs!