It will work fine. If any thing the CPU might bottleneck the GPU slightly in a few games but it won't be a whole lot.
The Radeon HD 7870 is quite a lot faster than the built-in Radeon HD 6550D on the APU.
The built-in graphics on the APU will be disabled when you install the 7850. However, Radeon HD 7870 cards are 2 slot cards so make sure that your motherboard and case have enough space.
How About the GTX 660 (non Ti) Superclocked Edition???Will it bottleneck my pc???
Yes any modern GPU over $100 will be held back to some extent on any APU.
Not the higher end A10-5700/5800k's you'd have to go to something like a HD 7950/7970 to bottleneck those. The Mid range and lower end stuff can keep up with about a HD 7850 or so.
@OP:
The HD 7870 will be fine for you, when we discuss a bottleneck, it's not really a negative thing so much. Basically it just means your GPU will be able to do a little more than your CPU will allow at the high end. So, in most games, you'll still get supremely playable results, but in CPU bound games, your frame rates will drop a little more than someone with a higher end CPU. Don't worry about it too much.