I don't know about the RAM configuration. I have a dual CPU machine (Dell Precision) that doesn't require the second bank to be populated, but HP's setup could be different.
But I do know that when you try to add a second CPU, it isn't enough to buy a CPU with the same model name and speed. You have to get the same stepping version. The CPU makers like Intel tweak and patch the CPUs throughout the production life cycle, and assign them stepping numbers, the first one typically being A-0. Most chipsets that support dual CPUs, at least the Intel ones like mine, will not tolerate a difference in the stepping numbers. We have often had to buy two matching CPUs when upgrading customers servers in the field because it wasn't possible to find a match to the one CPU that was installed.
You can check the stepping number with a number of tools, including CPUID from Intel.
James