no

An antimatter apple would explode violently when it came into contact with normal matter protons, electrons and neutrons making up he atmosphere.
If you could induce an antimater atmosphere to make the apple stabil, it would fall down the same because the force that creates gravity would be created by the realm of the antimatter.

Its like saying that in a universe of antimatter, light would be antilight. Light would be sucked into a star. Mass would repell and instead of stars coalescing to form, they would disolve.

With an apple I will astonish Paris.
Paul Cezanne


.. ....

The title of this post made me chuckle. I don't know whether or not it would fall up (or rise), but I do know I think it's interesting that physicists think it's worthy of study.

What makes it worthy of study is that if anti-matter did react as the question asks it would provide a technological direction to take for propulsion. But I rather think skwirl made a pretty good explanation why it wouldn't react that way.

What is the by-product of total annihilation?
Antimatter could 'fuel' a propulsion system in it's controlled combination with matter. The problem is that controlled collision would have to be controlled to the nanometer and the 'fuel' would need to be stored, shaved and induced into the combustion chamber in a total vacuum by magnetics.
The combustion chamber, the particle firing tube and the exhaust would all need to be able to withstand the energies that would be produced. Every aspect of the machine would have to be pristine as each particle is sent toward the combination reaction chamber. Yikes, if an errant atom makes its way into the holding chamber.

Matter and Anti-Matter are just forms of energy. Gravity, if you accept Dr. Albert Einstein's well tested theories, is a warping of space and time that only pulls. It pulls matter energy the same as anti-matter energy. If anti-matter were to 'fall up', that would require new theories to explain and completely destroy old theories. I don't find the concept plausible that anti-matter would react any differently than matter to the force of gravity. It should be exactly the same, but it has not been empirically observed yet, so the experiment is worth testing and proving.

If you want to learn about something controversial, read the Wikipedia article on Large Hadron Collider Safety at: http://en.wikipedia.org/wiki/Large_Hadron_Collider#Safety_concerns