Result: YES
YES! You can install custom firmware using kartdlphax.
(You will need to obtain a digital or cartridge copy of Mario Kart 7. The 3DS with CFW must also be (or be changed to) the region of the 3DS you are trying to mod.)
Go to Installing boot9strap (kartdlphax)
If you don't have or cannot obtain Mario Kart 7, other exploits exist involving Pokémon Omega Ruby/Alpha Sapphire, Paper Mario: Sticker Star, Ocarina of Time 3D, and Pokémon Super Mystery Dungeon. However, instructions for these exploits have not been entirely written and require that you own the physical cartridge.