Interestingly enough, this VMware article seems to state that Windows 2008 Web 32 bit and Windows 2003 Web 32bit are supported: It mentions "Windows 2003 all editions" and "Windows 2008 32 bit all editions. However, it is explicit in only stating Std/Ent versions of 64bit Windows 2008. I guess I can give it a try and hope VMware support doesn't pull a fast one on me if I ever contact them for help.
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5. Make sure your system has
all the software prerequisites for vCenter Server:+
Note:
For more information, see the vCenter Server Prerequisites section
of the ESX and vCenter Server Installation Guide.Make sure your operating system meets the requirements:
Note: For more information, see the Operating System Compatibility for
vSphere Client, vCenter Server, and VMware vCenter Update Manager section
of the VMware Infrastructure Compatibility Guide.+
Windows XP Pro SP2 (SP2 required)
Windows Server 2003, SP1 and SP2 32bit and 64bit all editions
Windows Server 2003, R2 and SP2 32bit and 64bit all editions
Windows Server 2008 32bit all editions
Windows Server 2008 64bit Standard and Enterprise editions+