A VkFence can be waited upon or queried about its state. Is it possible to have a callback invoked by the Vulkan implementation when the fence is ready instead?
This would allow it to be used with objects such as a std::condition_variable. When the fence would be ready, the condition_variable would get notified.
Such an approach would also allow integration with libraries like Boost.Fiber, which would completely remove the need for the thread to sleep, but rather it could do useful work while waiting upon the fence.
If this is not possible in base Vulkan, is there an extension that allows it?
Vulkan doesn't work that way. Vulkan devices and queues execute independently of the CPU. Indeed, with one or two exceptions, Vulkan implementations only ever use CPU resources within the scope of a particular function call and only on the thread on which this call was made. Even debug callbacks are made within the scope of the function that caused the error.
There is no mechanism for Vulkan implementations to use CPU resources without the explicit consent of the user of the API (again, minus one or two exceptions). So no callbacks that act outside of an API call.
Vulkan does have a way to extract a native synchronization object from a VkFence, but it is surprisingly not useful in Windows. While you can get a HANDLE, it cannot be used by the Win32 API for waiting on it. This is mainly for interop with other APIs (like converting it to a D3D12 sync object), not for waiting on it yourself. But the file descriptor extraction operation can get a fully functional sync object... if the implementation lets you.