Is the processor id got from systems.management unique?

I imagine you're talking here about the ProcessorId property of the Win32_Processor WMI class which, according to the documentation, is determined as follows:

" For an x86 class CPU, the field format depends on the processor support of the CPUID instruction. If the instruction is supported, the property contains 2 (two) DWORD formatted values. The first is an offset of 08h-0Bh, which is the EAX value that a CPUID instruction returns with input EAX set to 1. The second is an offset of 0Ch-0Fh, which is the EDX value that the instruction returns. Only the first two bytes of the property are significant and contain the contents of the DX register at CPU reset—all others are set to 0 (zero), and the contents are in DWORD format."

Clearly, this is not going to unique for each processor. It might be unique for a given type of processor but I don't think even that can be assumed.

I also found this SO thread where someone else has asked a similar question:

http://stackoverflow.com/questions/1101772/win32-processoris-processorid-unique-for-all-computers