This is a tough question; there is no easy yes or no answer. So many variables and factors.
First, there are many religions out there. There are historical religions, including many that are no longer practiced, but were once major religions. There are polytheistic religions and monotheistic ones. There are modern religions, such as Mormonism and Scientology... and even debate as to whether those, and others, constitute religions. What religion to we pick? Do we take a composite?
Second, there is the measurement problem. How do we measure overall good vs. bad impact? Certainly, we can cite many instances where religion has stalled human progress, has been regressive, even backwards, has been on the wrong side of history, has committed great injustices, and so on. On the other hand, religion has given humans some really good things like hope, morals, music, literature, architecture, and so on. Could these things have developed in absence of religion? Perhaps. Are there other things that could have provided us with this kind of compass? Assuredly. Can we ever be certain? No.
Since I'm no huge fan of religion, but still think that there are redeeming qualities about it, let's take one of my favourite tenets - the Golden Rule - as an example of the complexities of responding to the question posed. The Golden Rule states, "do unto others as they would do unto you." This is a viewpoint that religion has helped propagate (whether followers adhered to this is another matter). I think this is an outlook that makes a lot of sense, whether or not you're religious. For instance, many philosophers, including atheists, seem to advance some concept of the Golden Rule.
Admittedly, questions still abound. Would secular humanists arrived at a similar type of though in absence of religion? Would this idea have been shared?
To throw a curve-ball into the discussion, humans appear to desire some degree of understanding. In modernity, science has for the most part sought to explain things. However, there was a time where there were a great many mysteries facing humans and since science hadn't caught up with the questions being asked, perhaps religion helped fill that void. In that respect, religion could be viewed as a necessary stop-gap to help humans make sense of the universe until we had another methodology to do so.
In closing, perchance a more complex question is how has religion shaped our modern day moral viewpoints, whether we be theist or atheist?
(Full bias disclosure: I'm atheist and wasn't raised going to any particular church so I didn't have an overly religious upbringing. I do find many aspects of religion troubling, though. On the other hand, I'm not yet willing to write-off the entire experiment.)