Jay,
I have two different rifles that will shoot tiny little groups at 1000 yards as long as I do my part (doesn't happen often).
Either one will shoot ragged 1 hole groups at 100 (perhaps 1/4 to 3/8 moa) with my chosen 1000 yard load.
So far as what group size I would accept at 100 yards before shooting an animal at 1000 yards.
Answer: I would NEVER accept any sort of a 100 yard group for that sort of shooting. If you are going to try to cleanly shoot a living animal at 1000 yards you MUST know what that particular rifle, and yourself, are capable of shooting well past 1000 yards.
I shoot to 800 yards weekly and to 1000 yards perhaps 6 or 7 times a year. Personally, I would put my limit to shoot game at 500 yards because at longer yardages windage is by far the toughest component. You can get the bullet drop down to within 1/2 moa all the way out as far as you care to test loads and use a laser range finder to determine the exact distance to the target. To the best of my knowledge there is nothing besides skill, experience, and judgement which will allow you to accurately decide the wind drift at extended distances.
Misjudging the average windage by more than 1 mph at 1000 yards with a 308 Winchester (for instance) would mean a change in about 10" in bullet impact. That is enough to end up with a wounded animal rather than a clean and humane kill. Granted that most long range shooters use something more substantial than a 308 Winchester, but the concept still holds true that the windage component still governs where the bullet will hit in real world long range shooting.
That really leads to the question of what wind conditions would you consider appropriate for taking a 1000 yard shot at a game animal?
That distance is past my personal limit so I am interested in hearing what the heavy weights think.