Hi there,
I do not think you are out of luck yet - I can't guarantee that Quadro 4000 will work at least as vSGA but the following is the output of nVidia Shared Management Interface nvidia-smi inside the ESXi host and it looks quite promising:
/etc/init.d # nvidia-smi -h
NVIDIA System Management Interface -- v340.32
NVSMI provides monitoring information for Tesla and select Quadro devices. The data is presented in either a plain text or an XML format, via stdout or a file.NVSMI also provides several management operations for changing the device state. Note that the functionality of NVSMI is exposed through the NVML C-based library. See the NVIDIA developer website for more information about NVML. Python and Perl wrappers to NVML are also available. The output of NVSMI is not guaranteed to be backwards compatible; NVML and the bindings are backwards compatible.
Supported products:
- Full Support
- All Tesla products, starting with the Fermi architecture
- All Quadro products, starting with the Fermi architecture
- All GRID products, starting with the Kepler architecture
- Limited Support
- All Geforce products, starting with the Fermi architecture
Also, you can find the supported deviceIDs in its parsing file: 06dd NVIDIAQuadro 4000.
So theoretically if you install the nVidia VIB in your hypervisor, and on the next reboot xorg and NVIDIA Module startup is successful, you might reach the Shared VGA functionality - although with much lower ratio of users:desktop that nVidia Grid promises :smileyhappy:
If you decide to do that, please keep us updated and good luck!