I know that when it comes to playing NDS games, if you have the battery saver mode enabled the CycloDS lasts about as long as if you were playing the original game cartridge before you need to recharge the console.
But for GBA, I'm honestly not sure about battery life.
Edit: Actually, the game is stored on the EZ Flash 3-in-1 anyway - so the CycloDS battery isn't important. CycloDS Evolution and iEvolution do not play GBA games directly from slot 1.