When you remove Nintendo ID from 3DS, the console deletes the icons but the software still remains installed, save files included.
Sounds weird, I know, but this happened when I removed NID from my niece's 2DS. I got the usual warning that I would lose all games and whatnot. I didn't backup her saves beforehand with JKSM like an idiot. Had a mini heart attack and desperately went to install her game library via FreeShop. Lo and behold, FreeShop is telling me that all of her software was still there. All freeshop did was "pull them out", so to speak. I really don't understand the technical mumbo behind it, all I know is that removing NID does nothing to already installed software and save files.
Knowing this, I guess you would have to include the SD card if you want to include the software.