It won't have problems "running" as this is more dependent on the Operating System. Everything is a layered architecture. So if the OS can run on the h/w perfectly, and the s/w is designed to be run on the OS, you should be good.
"Performance" is another thing. I am not sure about Photoshop, but it probably can run well enough on an AMD. But the effect of h/w is quite visible at times.
Obviously, we all know that a "slow" CPU makes things run slow on ur system. And AMD processors that I own (Winnie, Venice generation) are terrible at multi-tasking. Whenever I do heavy simulations on my system, I can't even browse the web properly.
So while the h/w certainly affects performance, the "ability" to run is more dictated by the OS. Of course, if the h/w is "completely" junk, then the s/w might not even install saying your system isn't powerful enough.