My Animal Crossing: New Leaf 3DS came with AC:NL pre-installed, and I was wondering, if I were to purchase a new Animal Crossing New Leaf cartridge, would I be able to insert it into my 3DS (which already has the game pre-installed)? Would it count as a whole new game or would it continue the saved data from my pre-installed game? Or would it completely mess everything up? I'm sorry if this sounds confusing, but I just want to know if I could use a cartridge and have a whole separate game as if I had two 3DS's.
As the 3DS does not save cartidge save data to the system or SD card, there will be no clash between the two instances. They will be treated as separate games, with one file being on your download instance, and one on your cartridge.
StreetPass and SpotPass hits should go to both copies. Nintendo has fairly recently made available a tool to move save data from cartridge to download versions (albeit not the other way), so if you'd ever feel the need to do that it's completely possible.