However there is no uniform agreement on this and if you read below the grahic, South Africa's own Jim Davis on Avcom, has the following to say with his recommendation:
Actually there is no straight answer to this question because it is an type specific thing.
What I can tell you is that with many "modern" aircraft - including the entire Cherokee range - which is 50 years old - the handbook tells you that the ailerons are effective throughout the stall. This is absolutely correct. If you stall a Cherokee by holding the nose in the level attitude until she is fully stalled, you can use the ailerons just fine while she is shuddering and dropping the nose.
I can not speak for the Cessna 100 and 200 series, or the Beechcraft Bonanza, and Musketeer ranges, but I suspect they are the same.
The theory about the down-going aileron causing a larger angle of attack, and therefore stalling, is simply not correct. What happens is that the down-going aileron changes the aerofoil profile. It makes that part of the wing have a much larger camber, or curve. In fact it turns it into a wing that resists stalling at that angle. Don't believe me? Try this:
Fly your Cherokee, falpless, until it is just starting to shudder on the ragged edge of a stall. Now, without allowing the nose to move, suddenly apply full flap. According to conventional wisdom this should cause the wing to stall - because you have increased the angle of attack on that section. Actually the reverse happens - the flaps put you almost 10 kts above the stall.
HOWEVER don't expect ailerons to puck up a dropped wing in another types of aircraft - particularly the older ones - because many designers, at that stage, hadn't got round to protecting the pilots from their hammy flying!
I should also point out that when training new pilots, it is safer to teach them not to use aileron alone to pick up a dropped wing on the stall. Because that rule covers ALL bases.
In fact, you will get the most positive response by using coordinated aileron and rudder together, on all aircraft. I don't know of any exceptions.