Support for grahpics APIs happens at the driver level. The driver for your GPU needs to support Vulkan, not FreeBSD. So the real question is whether the driver for your make and model of GPU that's available for FreeBSD supports Vulkan. My guess would be "no."
If you’re a GeForce gamer, you already have what you need to take advantage of what the Vulkan API can do. If you’re a developer, you will now have the choice of a new tool that will give you more control, and greater performance, on a broad range of devices.