In the nutshell, what I understood looking into:
 Reading the following:
Video Acceleration API (VA API) interface architecture
The current interface is window system independent, so that it can potentially be used with graphics sub-systems other than the DRI (Direct Rendering Infrastructure) in X Window System, such as direct with framebuffer, and it can work with third-party DRM (Direct Rendering Manager) libraries. In a nutshell, it is a scheme to pass various types of data buffers from the application to the GPU for decoding or encoding a compressed bit-stream.
YES, your VA-API is independent, considering the following:
"The main motivation for VA-API (Video Acceleration API) is to enable hardware accelerated video decode/encode at various entry-points (VLD, IDCT, Motion Compensation etc.) for the prevailing coding standards today (MPEG-2, MPEG-4 ASP/H.263, MPEG-4 AVC/H.264, H.265/HEVC and VC-1/VMW3)." http://www.freedesktop.org/wiki/Software/vaapi
In other words, VA-API is INDEPENDENT
of X11 Server just to manipulate the video streaming
(coding/decoding), nothing more.
But for your DP and screen to work, you HAVE TO HAVE X11 Server -> Compositor (to move several/many Xwindows around and show them on the screen).
Let me throw wild guess why, after you removed the monitor, these VA-API I/Fs do not work: probably they need/require (?) monitor's EDID (basic video sync timings for your monitor), so if you return monitor, and reboot, everything (probably) will behave correctly (in regards to VA-APIs), as before.
The trick here is, if monitor's EDID not provided via DDC/CI interface, VA-API is going to (probably
) ask X11 Server to provide back generic EDID.