There is overhead but Vulkan allows you to batch draw calls in a far more efficient manner. It can also generally use multi threading to feed a GPU even if the game isn't coded with that in mind. Basically Vulkan offers so many improvements to efficiency and parallelization that the overhead is a drop in the bucket compared to the overall speedup in draw call optimization alone.
There is overhead but Vulkan allows you to batch draw calls in a far more efficient manner. It can also generally use multi threading to feed a GPU even if the game isn't coded with that in mind. Basically Vulkan offers so many improvements to efficiency and parallelization that the overhead is a drop in the bucket compared to the overall speedup in draw call optimization alone.