It just so happens the GX620 USFF that I'm using at this moment is happily running a Pentium D 3.4. That's the limit for all of the GX620s, but the Pentium D is, indeed, dual core.
You are correct. I shouldn't have refered to it as being in the single core era. I forgot about the early Pentium D being a dual core. But in my defense, the OP asked about a Core 2 Duo processor. I don't believe the machine can handle that even if it has a LGA 775 socket. Knowing which motherboard the computer has would be helpful.