Hello.   As long as the processors have matching specifications, it is fine.   Yes, each processor or CPU should have identical or mirrored memory. Hence, the memory on the populated channels have to be identical for optimal memory configuration.   
First time post!  Our organization currently has 2 Poweredge T610 servers.  We just moved the VM's to one of them, and will not be using the 2nd T610.  So my question is this.  It is a dual processor capable board with 1xIntel Xeon2.66Ghz CPU, so it is feasible to transfer the CPU from the old to the new T610?  Both use the same pn# CPU - an Intel Xeon  E5640 2.66Ghz.  The other question is this.   If it is possible, then we need to mirror the ram to be the same on both sides (currently has 24GB).  If so, we would be set with 12GB on each side.  The system would still see the total of 24GB addressable, correct?
T610 2nd Processor upgrade