It should work, but the problem is that the float valve will restrict the filling of the butt to a mere dribble as there will be very little 'head', so it will be difficult to keep the butt topped up. These divertors are relatively inefficient as they cannot cope with a large flow due to the typically 1" diameter pipe. If possible arrange for the down pipe to go into the butt with a suitably large overflow into the drain, I've used 40mm waste pipe for my overflow, and it's very rare that this doesn't cope. You might be able to get 40mm across the bottom of the door to the existing drain/soakaway?
Peter