I had the CCC originally on a fairly large SATA drive I was using as my C: drive, but then I decided to swap that out for a nice shiny new 250 GB SSD, and didn't want CCC filling it up with all of its stuff, so I just altered the location and manually copied everything over to it, and it never lost a beat finding its 'stuff', so it was all quite seamless and painless.
I believe that as long as you have the path information correct, and put the data into wherever you moved it to, it should run fine - whether you are doing as I did above, or are similarly moving to a new PC.
Best of luck with your fancy new computer - Hope you load it up with lots and lots of new toys, and have a blast with it all. :)
Bob Bone