A zygote would not pass its "self-test". Embryos screen for several genetic conditions, including impotent mitochondria. The lysosomes of the developing child will explode and apopstosis or "programmed cell suicide" will occur. Theoretically however, an organism could live for a short time without mitochondria. We would just undergo anaerobic respiration but eventuall atrophy from the lactic acid by product. Please read about the Electron transport chain (to understand the importance of mitchondrion) and feel free to comment me if you would like a copy of an article I recently wrote about it.