I'm using Radeon R9 390 as OpenCL co-processor with no display connected (monitor is plugged into Intel HD 530), but the card still consumes 17W in idle what doesn't look like ZeroCore state. Screenshot after boot, no OpenCL tasks run yet. System: Win2008R2, drivers: any recent version, currently at Vulkan-Beta-Feb17.
Also it's very annoying that Crimson driver installer doesn't automatically install any control panel on Win2008R2. Manual install from the depth of C:\AMD folder works with no issues.