No, at least not with our species as it is now. Our planet cannot support the population it has now on the amount of resources it provides. Until then we will not have enough food or shelter for stability. And...even if we did there would still be greedy people who would forcibly take too much and cause instability. Under communism there is no real way for the community to deal with injustice. If there is a police force or a group to govern them, then it isn't communism, it's socialism.