First, humans have been on this planet for at least 100,000 years. If we are talking about the dominant religions, they’ve only been around for at most 4,000 years in the case of precursors to Judaism. So for 96,000 years we as a species had to get along with other members of our group and deal with people who are unfair or dangerous etc…We simply wouldn’t have persisted as a social primate without some rules of behaviour.
There is fascinating discussion by Sam Harris about the basis for finding an objective source of morality at this link.
http://thesciencenetwork.org/programs/beyond-belief-candles-in-the-dark/sam-harris-1
Second, we aren’t flying blind with regards to this question, because we already have a test going on this very minute in Scandinavia.
HIghest organic (voluntary) atheism in the world. For instance, less than 20% believe in a personal god in Sweden.
So, are these moral societies? I would argue yes based on the argument that morality and ethics at their core are about decreasing suffering, promoting equality, which thus enables most people to and lead happy lives. If we look at Scandinavia it is a bastion of universal health care, no death penalty, some fo the highest levels of societal happiness, sexual equality, long-life expectancy, low corruption, low child mortality, low murder rates, high refugee intakes, low STD rates, high expenditure on foreign aid, etc. etc..
I doubt we will all agree about morality but these seem to have at least something to do with the issue, and things are going along just fine in these societies that are dominated by agnostics and atheists. If religion was necessary for morality in all societies, then we shouldn’t see exceptions like this.
Phil Zuckerman has a book out called Society without God, which examines this very question based on Scandinavia
Third, is the argument that we should see higher rates of crime being committed by atheists. This is not the case, but is probably confounded by different socio-economic /educational levels.