Nope. You need an EZ Flash 3-in-1 to do that. Or a SuperCard DSTwo or an EZ Flash IV. There is a GBA emulator out for DSi, but it isn't any good as of now. - http://gbatemp.net/t281715-gba-emulator-for-ds-i
That's GameBoy and GameBoy Color. This is about GameBoy Advance. Those are all different systems. GBA can not be played on a regular flashcart.