You'll probably sink in (and have a bad day.)
The longer answer is that it depends on how you land. Force from a touchdown on a runway can vary from nearly zero (in an extremely light landing) all the way up to twice the weight of the aircraft or more (in a hard landing.)
While it's theoretically possible to land an airplane very lightly on the runway, this normally requires a high forward speed and a very low vertical speed. It's rather unlikely that an incident resulting in landing short of the threshold (on the EMAS) would be at such a low vertical speed and high forward speed. The opposite situation (low forward speed, high vertical speed compared to a normal touchdown) is more likely in a situation of touching down short of the runway, otherwise you'd have probably made the runway.
As a result of this, the kind of landing that is likely to result in a touchdown short of the runway will result in forces that are minimally a significant fraction of the aircraft's weight and quite possibly at or significantly above that weight. Since the EMAS is guaranteed to buckle at less than the aircraft's weight in an overrun situation, it would almost certainly do so in the situation of landing on it.
The momentum of the airplane (specifically, the downward component of its momentum) will actually make it more likely for it to sink into the EMAS on touchdown, not less.
Of course, EMAS isn't designed for anything near the touchdown speed of an airliner. According to FAA Advisory Circular 150/5220-22B, a standard EMAS is designed to stop an aircraft that overruns the runway at 70 knots or less. A landing airliner will be flying much faster than that (Peter's answer here says 160 knots for a 747, for example.) This means that the backwards acceleration applied to the airplane by the EMAS will probably exceed the design forces by quite a lot, making for a quite uncomfortable landing for the passengers and quite likely breaking things on the landing gear (if not just breaking the gear completely off.)
The answer from Peter that I linked above also mentions that, in a hard landing where no flare is performed, the average force applied to the runway during touchdown would be just under twice the weight of the aircraft in the case of a 747, so that helps to provide a rough idea of the upper bound of the vertical forces imparted on the surface by an airliner at touchdown relative to the aircraft's normal weight.