I manage a bunch of ESX and ESXi clusters. What the OP wants to do is... for lack of a better word, useless. If you have GPU cards in a server/workstation then you should just install LinuxCoin on that box and run your miners. Installing ESX/i doesn't give you any benefit, even if it were possible to get the drivers to work with the GPUs, because the whole point of ESX is to virtualize hardware. Since by definition you cannot virtualize GPU resources, and even then miners use 100% of the GPU resources anyway, there's NO REASON TO USE VIRTUALIZATION TO MINE.
Let's step through the BS in your post
1. "useless"? I have numerous VMs across multiple ESXi systems and need to keep them running, that is high power readily available hardware prime for GPUs. I need to keep ESXi running so why wouldn't I try and leverage the hardware on hand and do what the OP is looking to do.
2. You can virtualize GPU resources at varying levels between hypervisors however at this time not OpenCL. In this case pass that GPU directly to the VM itself using VT-d or IOMMU letting the VM execute whatever it wants on the GPU.
break break...
To address the OPs question, I have a couple of ESXi systems myself and was thinking the same thing since it's hardware. The primary issue is the stack of software you need to talk to the card, one can hack some packages into ESXi but you need X windows running with the fglrx driver. That requirement means you will need a large stack of packages to get it moving and would need to start hacking in a big way, start by researching whether or not it's even possible to get X running on ESXi itself.
Sadly my ESXi systems do not support VT-d/IOMMU or I would install my GPUs, map them to a VM and run my miners there.