The only thing After Effects uses a GPU to accelerate is the ray-traced renderer.
The bad news: the ray-traced renderer can only be accelerated by certain NVIDIA cards as it's based on NVIDIA technology. You cannot use an AMD card to accelerate it.
The good news: in After Effects CC, the ray-traced renderer became obsolete. AE now includes Cinema 4D Lite. This renders faster and is much more powerful than the ray-traced renderer.
So, if you're using After Effects CC (or the brand new After Effects CC 2014), you can use that card. Well, unless you are using Premiere or certain third-party plugins to After Effects (like VideoCopilot's , they all have different requirements.