Would a amd fx 8320e bottleneck my gtx 970?

Solution
I do not know what you have now.
But, if you already have a FX of some sort as well as a GTX970, I think you are unlikely to see any difference using a FX-8320e.
For example, a FX-6300 has a passmark rating of 6345 and a single thread rating of 1409.
The FX-8320e has a passmark rating of 7430 and a single thread rating of 1350

Few games can use more than 2-3 cores, so the extra cores are not helpful. Possibly helpful if your BF4 is multiplayer.
But really, most games are dependent on the strength of a single master core so I would expect no real change.
At stock, probably not. With a decent OC and good supporting components like fast RAM, definitely not. 970 is geared toward 1080p-1440p 60FPS gaming.

Here's an example:

[video="https://www.youtube.com/watch?v=4ZHlo0DAI38"]https://www.youtube.com/watch?v=4ZHlo0DAI38[/video]
 
I do not know what you have now.
But, if you already have a FX of some sort as well as a GTX970, I think you are unlikely to see any difference using a FX-8320e.
For example, a FX-6300 has a passmark rating of 6345 and a single thread rating of 1409.
The FX-8320e has a passmark rating of 7430 and a single thread rating of 1350

Few games can use more than 2-3 cores, so the extra cores are not helpful. Possibly helpful if your BF4 is multiplayer.
But really, most games are dependent on the strength of a single master core so I would expect no real change.
 
Solution

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I have a 8320e @ 4.5Ghz with 16gb ram @ 1728MHZ with 970 SLI on a Asus 970 Pro Gaming MB. It easily handles anything I throw at it. Yes, not overclocked it will bottleneck but around 4.2ghz it shouldn't and it should be easily to overclock 1 Ghz. I have my voltage at 1.38 @ 4.5Ghz stable and could go higher.

Single 970 Firestrike score is 9300. SLI is 13000. The 8 core processors are pretty much all the same exact clock speed and the E series is more efficient. There are a lot of hardware sites that have the 8320e overclocked high for benchmarks. My passmark score is 10,500.