I suspect it would be quite the accomplishment to kill a deer with an atlatl. Given the amount of movement that is necessary, it would be pretty hard to get the drop on a deer. However, with the size of the bolts, I bet they have some serious kinetic energy when they find their target. Personally, I think it's cool. It's a true primitive weapon, unlike modern compound bows and muzzleloaders.
My only concern with it is that due to the difficulty of use and some people's laziness, you might end up with some injured deer that aren't recovered. But, the same thing happens with rifles, shotguns, and bows and there'll be a lot more of those in the woods than there will be atlatls. So I say, go for it.