With a few exceptions, like the extra power in DSi Player (Not a flashcart) and DSTwo, Emulating GBA through a Slot 1 cart on the DS is impossible.
What the Cyclo does is, it uses its GUI to load the GBA rom into the EZ 3in1, and then the 3in1 runs the rom off it's memory as a GBA game in GBA mode.
Once in GBA mode, the Cyclo part of this process is dead. You can even take the Cyclo out and the game is running. Once you start Cyclo again, it copies the temporary save file of the GBA game you played, and stores it on your SD card.
EZ 3in1 doesn't have a GUI of its own to my knowledge; it just does all the GBA work while Cyclo is the manager.