Well, with a magic light source providing energy (like the ones already mentioned) it might be possible, though you would need to really expand the bag of holding extradimensional if your going to produce enough net oxygen for even just a halfling. It technically isn't a closed system with a light source. There must be a way to rig it so you get net oxygen, as on Starship Earth, because without it, we 02 breathing animals wouldn't survive.

NASA is doing some similar experiments, though without the bag of holding.