I do this all the time. I actually save each of my virtual machines in a separate directory and duplicate the entire directory to make a copy. All links in the VMX file (configuration) refer to the current directory.
One thing to watch out for. The VMX file has a line with the MAC address of the virtual network card:
ethernet0.generatedAddress = "00:0c:29:ff:1f:c7"
, - 1 ( c8).
displayName , , .