I guess the subject says it all: would switching to Windows HPC Server 2008 R2 have any effect on average network latency ping times? Even if it shaved a few milliseconds off the time, I'd be happy - but is that realistic?
The only thing that HPC would change in the networking stack is RDMA (Remote Direct Memory Access), which is used in computing clusters. Normal network operations are not changed.
If you're looking to shave latency, consider purchasing a NIC with a full TCP Offload Engine (TOE).
Also of note is this quote from the HPC FAQ:
"Both Windows HPC Server 2008 R2 Suite and Windows Server 2008 R2 HPC Edition are licensed solely for running clustered HPC (high performance computing) applications."
Changing your OS is unlikely to have a net effect on ping times -- Latency is affected by the following factors (not a comprehensive list, but in a rough kind of order)
There's very little you can do about 1 & 2. You can look after 3 within your own walls. Changing anything below about #4 is usually subject to diminishing returns ; there's nothing you can do about 7, 8 or 9.