I could shoot them pretty regularly in archery deer season, either from a treestand or while still-hunting. Obvioulsy, I'm not calling them at this time of year as I'm deer hunting.
I'd say I could still-hunt them with good success in the spring too, but the fun of spring turkey hunting is the calling. I don't really want to ambush them in the spring. When you are calling, the bird is looking for you, and its hard to conceal all of the movement required to draw a bow without a blind. Anything is possible though.