Swapnote is 3DSWare, so it saves to the SD card if you download it from the store, like all 3DSWare. The system only saves certain applications to the system memory. And before anyone points out the DSiWare installs to the internal memory, DSiWare installs to the internal memory and can be moved to the SD but can't be run from the SD card. EDIT: The 3DS titles and 3DSWare can be played from the SDCard, which is why the system saves them there. DSiWare is designed NOT to play from the SD card but from internal memory. So that's why it will save directly to system memory.
Whether or not Swapnote is installed to system memory is... hard to say. Most items that you start with are saved to your system memory, so I assume Swapnote is as well, considering that I never uninstalled SwapNote but I can take out my SD card and still have it (none of my messages, though). But just so you know, items in the internal memory aren't permanent-- you can move data into and out of system memory no problem, you just can't delete some items (Face Raiders, for example). I doubt the manufacturing process involves downloading software-- it probably comes in your system memory initially because they would be placing it with a bunch of other 3DSWare.
But after you delete it, since you can only get it from the eShop it, like all other 3DSWare titles, will save to the SDCard.