In games, the CPU prepares tasks to feed the GPUs.
For DX11/OpenGL, there's an "Immediate Context" running on a main thread. This context talks to the driver alone and the driver will send the tasks to the GPU for processing. However, by only using a single thread, it might not have enough work to be submitted to the GPU.
If the game has multithreading support, it will use several threads to prepare "Deferred Contexts". This deferred/secondary context will submit the task to the "Immediate Context" so it can be sent to the driver and then to GPU for processing.
If the game or the driver doesn't support "Deferred Context/Command List", there will be a lot of holes in the "Immediate Context" causing it to be unable to feed the GPU with enough work, resulting in "CPU bottleneck".
This is also why AMD driver that doesn't support DX11 command list has "high driver overhead". (Well, it is supported only for some DX11 games)
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In other words, all threads talk to the main thread (parallel) -> main thread talk to driver (serial) -> driver talk to GPU (serial) -> GPU process
In DX12/Vulkan, this "Immediate Context" middleman is removed. All threads can submit tasks in parallel to the driver through the use of queue. The driver will then submit the task to the GPU.
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In other words, all threads talk to driver (parallel) -> driver talk to GPU (serial) -> GPU process
Note: In DX11/DX12/Vulkan etc, the driver still submits the tasks(command list) to the GPU in serial. However, this submission is very efficient. So, it's very low in overhead.
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CPU bottleneck happens if there is not enough work to feed the GPU, either due to the lack of good threading or driver overhead or CPU is simply not fast enough.
In the case of GPU bottleneck, it means the GPU can't complete all the tasks fast enough.
In the end, it depends on how the developers code the game.
In DX11, some games don't exploit the deferred context too much resulting in lightly threaded code i.e. both CPU and GPU has low utilization.. In this case, faster IPC and clock speed will benefit more than higher core count.
TLDR: It is very hard to just generalize "Will this CPU bottleneck my GPU?". It depends on different games.