PhysX is a physics library, which uses either the CPU or GPU to perform calculations. The latter option requires a proprietary nVidia API called CUDA. The former option performed poorly in older PhysX releases, and performs relatively well in current releases (best case is probably Borderlands 2).
What you're asking is whether AMD can have a physics library run on the GPU. That will happen as soon as some software library is ported to a standard like OpenCL or DirectCompute.
PhysX itself could go that route, but given the corporate culture of nVidia, that seems extremely unlikely.
Havok is by far the most common physics library in use, and porting that to OpenCL or DirectCompute would be huge. I'm not aware of any plans towards that end.
Bullet is a relatively new physics library that's under active development and supports OpenCL. There's potential there, but the main market penetration seems to be mobile apps right now.
And once Havok or Bullet become viable options for GPU-accelerated physics, it's up to the game developers to choose them over PhysX. Given that Havok will be looking for licensing fees and Bullet will require paying someone for support (it's open source), while nVidia will be pushing PhysX with cash in hand, it will still be an uphill battle.
I wouldn't expect physics calculations on AMD GPU's for a year or two at minimum.