Will CNC work with an APU?

I don't think it matters as much since it is an in browser game. So it's more of a browser compatibility question.

I would say yes.

I have got ta to run on a single core intel and a modern browser. Not very well but it ran.

That multicore amd should have no problems 

Assuming the Original Poster is referring to Command and Conquer: Tiberium Alliances and not one of the many others in the franchise then I agree - the biggest issues are going to be compatibility with the browser followed by available memory and internet connectivity.

The processor is not often an issue with CnC:TA