Using a Cyber Gadget CodeFreak game capture utility, one YouTube user has found the 3DS will run backed-up games and even homebrew applications. In the videos past the break, you can see it using the Game & Watch Collection to launch unsigned code, including a copied version of Mario Kart DS and the Lameboy emulator.
Additionally, it would seem the R4 cart also yielded results on the 3DS. Another YouTube user has discovered that right now the 3DS will played backed-up games from an R4, since it recognizes it as a DS cartridge. Of course, Nintendo could kill compatibility at any time through a system update.