I've called cows in every week of bow season. One week hasn't seemed any better than another for me at least. However, where I hunt I don't go more than a mile from the rig the first week or so. I am usually by myself so if the weathers warm the pack out can be interesting. I usually hunt the least the first week of bow season due to warm conditions.
I'm usually so anxious to get out and hunt by the time Sept. comes around that I hunt it pretty hard right away. As other people have said, elk can be found any time of the year. One reason I like earlier is because you are more likely to find a stray cow or two away from a larger herd, which means they will react more to a call and will not have 100 eyes watching their back. However, it is tough to beat chasing vocal elk herds. If I had to choose, I would say Sept 15 every year.
One thing I've noticed in the unit I hunt in Colorado is that the first couple of weeks of archery season seem to have less hunting pressure. And although the elk aren't really rutting yet, they are in a summer routine that presents some ambush possibilities, I believe. So, there are some advantages to hunting early.