Sound Card in vSphere Virtual Machine is an unsupported configuration. This is feature dedicated to Virtual Machines created in VMware Workstation. However, you can still add HD Audio device to vSphere Virtual Machine by manually editing .vmx file. I have tested it in our lab environment and it works just fine.
Below procedure how to do this:
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1. Verify storage where VM with no soundcard reside
Make a backup copy of the .vmx file. If your edits break the virtual machine, you can roll back to the original version of the file.
More information about editing files on ESXi host, refer to KB article: https://kb.vmware.com/kb/1020302
If you go to “Edit Settings” of the VM, you can see information that device is unsupported. Please be aware that if after adding sound card to you virtual machine, you may exprience any kind of unexpected behavior (tip: in our lab env work this config without issues).