The DS lacks the 5V supply that the GB/GBC wants. While I can not in turn rule out said GB/GBC carts being able to be powered from 3.3V, and as you can presumably still write data to various pins having said signals do some programming I would look to the ever present question and response in the GBA era of "can I use my GBA flash cart to play GB/GBC games but not emulated?".
I imagine you could go one step further and make a GB bridge type device* that could take signals from the GBA slot and transform them somehow to have it work, however at that point it is probably easier to find another way.
*the gb bridge was a device that allowed certain GBA flash carts to function as GB/GBC carts, more http://www.gameboy-advance.net/flash_card/gb_bridge.htm . I have not pulled one apart to see how it works but changing voltage levels for signals and remapping things is not a radical concept within electronics.
Short version. Likely not without extra hardware, that also has not been designed yet. Certainly no pop this software on your DS flash cart and go to town type solution I am aware of.
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