Sure it can, there are animals that are technically immortal, there is a jellyfish that basically can live forever. If the jellyfish is injured or sick, it returns to its polyp stage over a three-day period, transforming its cells into a younger state that will eventually grow into adulthood all over again. So in terms of possibility, we definitely can.

I personally would like it, everyone would be immortal too so you don't need to worry about your loved ones dying and there is always something new to do.