No, but you can move files on an SD card or whatever, so that a different ROM is the one "seen" by the 3DS mode Gateway. It could be that between every boot, the Gateway "resets" (assuming it has some on board CPU to do this job, which it probably doesn't) and works as a DS-mode flash card, lets you select a game and "sets" that game, then reboots the 3DS and the Gateway acts as that game until the next power cycle when it becomes a DS-mode flash card again.
Now I don't think this would be possible without an on-board CPU to "reset" it back to DS-mode, and there's no sign that it has one, so I doubt this will be the case. But there's no proof it couldn't happen.