Depends on the CPU you are using, if the Linux kernel version 3.2.x supports that CPU. That is independent of Linux Mint.
Will it use all 8 cores or more? No, Linux Mint doesn't generate that much load on a system to actually need 8 or more cores to run
If the CPU is supported, and you give it something actual to do (like BOINC or Blender), you may generate enough load to actually occupy all 8 or more cores.
As for the server, Linux Mint 13 will run on supported hardware. So you can run it on a real server (if hardware is supported by the Linux kernel 3.2.x) or a virtual server as you desire. It is not intended to be run without a GUI though, so perhaps not the best fit for using as a server. Debian Stable would be better suited for that.