When I stump shoot, I tend to be more accurate than when I shoot at paper targets of any type. Of course, this is somewhat of a subjective judgement, since nobody is keeping score on pine cones. But I'm pretty sure I hit pine cones more often than I hit bulls eyes. I believe this is true even though I never know the distance to a pine cone, and I either know the marked distance to a regular target, or have shot the range enough that I have a pretty good idea of how far away a regular target is that we might shoot at an unmarked distance.
I think the reason for this is that I only carry one judo in my quiver, so I only get one shot at a pine cone before I have to go and pick up the arrow. Plus of course we don't shoot just at pine cones; we shoot at plastic bottles and a lot of other things like Terry mentioned, so that most targets are unique in some way or another, rather than just being another bulls eye. For those reasons, I think my concentration is ramped up to a higher level than it is when I'm shooting my third arrow at a 45 yard bulls eye target.
However, I think there are good reasons to shoot at both types of targets. I may not have the same level of concentration when I'm shooting my third arrow at a 45 yard bulls eye target, but if the third arrow is more than a normal deviation away from the bulls eye, it gives me a chance to reflect on the reason why, and to increase my awareness of what my body is doing more than I can when all my concentration is focused on a pine cone. I've shot at marked yardage targets at ranges up to 50 yards so much that I can get a lot of the same benefits, and a lot less boredom, than I could shooting at a blank bale at 5 yards and focusing solely on my form. When I'm shooting at a 45 yard bulls eye during my regular morning shoot, I'm thinking a lot more about my form than I am concentrating on hitting the bulls eye. Which generally means that I don't have very many bad shots that are off the target, but I don't have a whole lot of bulls eyes either.
I try to ramp up my concentration when I shoot in a tournament and make every shot a pine cone shot. Sometimes that works and I either win or place in my division, and sometimes it doesn't and I would be better off just focusing on my form like I do every morning. But I'm pretty sure I wouldn't win any tournaments that way.