It is possible, but you need the ez flash 3in1 expansion pack that goes in the gba slot along with extra software
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No, there isn't and will probably never be a GBA emulator for slot-1 flash carts.
Slot-2 ones should be able to support it though.
No, the R4DS is not capable of playing GBA games. You will need to buy a DS Flash Card such as the M3 Lite. It can be found at the following link. http://www.m3adapter.com/