First, let me ask you this, what moral system do you currently subscribe to? For the sake of argument, I'm going to assume that you beleive in the modern western world view of morality.
Ok, with that out of the way, lets get to the meat of this issue. My answer to your question is a resounding NO. Let me explain as to why this is the case.
I'll begin by saying that the current western world view of morality was founded by Christianity. Yes it was and you can argue with me on that point if you like, but whether you want to believe it or not, it is true. So to put it simply, today's standards of "all people are equal" and "everyone is special" etc etc etc all came from a religious orginization.
So, based on that point i strongly believe, that with out a religious foundation, the morals above it cannot and will not stand the test of time. For example, I see it in the following way:
Immagine you built a beautiful castle on top of some extremely strong bedrock, but a few yeaar down the road, you think it'll be a good idea to demolish said bed rock, but you still expect your castle to be in good shape. (in case you weren't aware, the castle in that scenario were morals, and the bedrock was religion)
My second point as to why are current morals will fail without religion is the common sense argument. Lately, I've been hearing alot of people going on about how "common sense will always allow people to make the right decisions." And frankly, this is just not the case. Common sense is not so common as most people believe, and honestly, we currently believe many things that don't follow the rules of common sense. Allow me to explain.
My first point on common sense's actually rarity is a little difficult to prove to most, but when you think about it, people all over the world do things that don't follow common sense, and this generally applies to people acting in their own self interest. Consider the person who goes out to a bar to drink. They end up overdrinking and being hungover and in pain the next day. Common sense says to not do that again, but will they? Of course they will!
My second point on common sense is that we believe alot of things that contradict common sense. For example, common sense says that the earth is standing still and the sun and moon rotate around it. But, we have all come to accept that the earth is hurtling at ridiculously fast speeds through the universe and that the sun is a giant ball of fire billions of miles away. Why do we believe this? Not common sense, but because our teachers told us so. In a way, we take it on blind faith that this is so. I doubt that many of us have actually gone into orbit to verify this fact.
So, getting back on topic, common sense really wouldn't be that great of a moral compass if it ever were to replace religion.
I could go on to explain why atheism is wrong and that there is a God and Galileo was wrong, but then I'd be here all night.