That CPU is shockingly similar to mine, differing only in that the Q6600 I've overclocked with the 333MHz FSB runs at 3.0GHz. I'm running an R9 280X, which is also surprisingly similar to the R9 380 (the 380 is a bit better), and I'm rather happy with it.
Given what a bottleneck means, I don't think you'll notice it. What a bottleneck means is that upgrading the GPU doesn't yield better performance since the CPU is a bottleneck, games only perform as much as the CPU allows it. What this means is two fold:
A better GPU doesn't improve performance. If the CPU is the bottleneck, then an R9 380 would perform the same as a Titan X SLI setup. This also means overclocking the GPU does nothing. In fact, underclocking the GPU may not decrease performance either.
A better CPU does improve performance. If the CPU is the bottleneck, then the R9 380 is not being fully utilized so by upgrading the CPU the potential of the GPU is unleashed, so to speak. This also means that overclocking the CPU leads to direct performance gains in games.
The easiest way to figure out if you have a bottleneck is to monitor the CPU and GPU usage in game. If you see the GPU at 50% but the CPU at 100%, then the CPU is holding you back. If you see the GPU at 100% and the CPU at 50%, then the GPU is holding you back. However, make no mistake in the second case it means you're getting everything your GPU has to offer, so if you are unhappy with the performance in that case then the GPU is the only part you need to upgrade. Actually in that case it means you purchased a GPU that wasn't up for what you intended to do to start with.
Even at the highest end, systems are either CPU bound or GPU bound. No system is unbound, the question is more about what kind of boundedness they have. If they're stuck at playing dual screen 4K at 60fps, that *is* a limit on what the machine can do. And if in doing so the GPUs are at 100% and the CPU is at 75% that system *is* GPU bottlenecked. But is anyone really going to be upset with 8K @ 60fps?
For your system, I wouldn't expect you'll get 1080p @ 60fps, but are you upset with 1080p @ 45fps? You'll be able to get more out of it when you upgrade the CPU, so provided you intend to do that sometime in the life of this card I think it's a good idea. If not, then you may find that a cheaper/less powerful card will give you the same performance because the CPU is a bottleneck (and like I said, all systems are bottlenecked by something to panic over or think that you'll see no improvement from the HD4870 -- I upgraded from an HD4890 and there's a huge improvement).
Personally, I've waited so long on a CPU/motherboard/RAM upgrade that I think when I do that I'm just going to go a bit over the top. At the moment I'd go with X99, 5930K, 32GB, and PCIe SSD. Depending on what Skylake-E offers, I may do that, but 6C/12T is definitely something I would make use of as I run a lot of virtual machines so 4C/8T Skylake is not appealing.
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