Not all, but most, yes. Bikes with a very relaxed steering geometry will not wobble (think cruiser type bikes), but they don't turn into a corner worth a shit either. In steering geometry there is an inherent compromise between quickness and stability. As you improve one you degrade the other.
The wobbling comes because the stability is low enough that the tiny deflections caused by worn tires put the steered mass into mechanical oscillation. You can get rid of it by putting new tires on because that removes the tiny deflections. Or you can get rid of it by putting more preload on the steering head bearings (or putting roller bearings in) because that increases the mechanical damping of the system, making it more stable.
The reason you first feel the wobbles while decelerating is because the bike and rider's weight is pitched forward on the bike, compressing the front fork and unweighting the rear shock. This temporarily sharpens the steering angles and makes the front less stable and more prone to oscillation. It goes to reason that you can get rid of the wobbles by increasing those steering angles, either by raising the front ride height (increase the preload), or lowering the rear (decrease the preload) or both. Unlike the ES, it is not easy to lower the rear ride height on an "A" model other than flipping the hard soft lever to soft (if it isn't already), but the front has 15mm of adjustment on the forks. Crank in some more preload up front and see how that affects the wobbles.
