Yes, if the VRAM is more than 1GB it would accelerate using CUDA with your GTX 970 card.
As I can see the VRAM on this card is 4GB.
It will accelerate stuff in Premiere, but not After Effects.
The only thing the GPU really accelerates in After Effects is the (obsolete) ray-traced renderer. More details here: GPU (CUDA, OpenGL) features in After Effects
And (not that it matters because you have more powerful 3d options in the current version of AE,) the 900 series cards DO NOT work to accelerate the ray-traced renderer. The ray-traced renderer works using NVIDIA's Optix library. NVIDIA changed that library on their newest cards and the new cards will not work to accelerate the ray-traced renderer. Since the After Effects team isn't putting any more development into the ray-traced renderer, new cards aren't going to work with it.
This page has the list of approved cards for accelerating the ray-traced renderer if you really want to use it for some reason.
Now, some third-party effects DO make use of the GPU (Red Giant's Universe, Video Copilot's Element 3d, Mettle's ShapeShifter, etc.), but AE's requirements have no bearing on that and the GTX 970 will work nicely with them.
Also, Premiere makes much use of the GPU so, if you use Premiere, check their requirements.
For some reason, I can't get to your link (no doubt, due to restrictions on the network where I work), so I can't comment on any of the other aspects of that computer. How much RAM is in it, what kind of hard drives, processor speed, etc.
The GPU is a GTX 970 4GB with about 1600 CUDA cores. 16GB if RAM. Intel Core i5-4690 (3.5GHz), 2TB HDD, 256GB SSD, z97-pro motherboard
GPU is almost pointless for standard AE (as mentioned) and if you did want to use the ray-traced renderer, that card will not accelerate it.
I'd recommend doubling the RAM. RAM is cheap and makes a difference.
Nice core speed on the processor. How many cores does it have?
Hard drives look good. Using an SSD for AE's cache makes a big difference.
The processor is 4-core and it happens to be the best i5 out there. Now I will upgrade the RAM once I need more, but for now I am on a budget so 16GBs are just fine.