You can do that. I recently got a new PC, and I copied my TS3 Documents and Program files folder over to my external drive before I set up my new one.
If you want to put the folders back on your new PC you need to install the game first, because as @Cororon said, it will need to add registry entries, but once it is done you can just overwrite your existing new folders with the old ones.
However, I would make a backup of the fresh new install folders first, just to be on the safe side.
Edit - Also, if you've had any kinds of issues with your old game setup, and you replace your new install folders with old, you're copying across all the problems as well as previous settings and such. I just felt I should mention that too.
Bear in mind, there is a line in your Options.ini in the TS3 Documents folder that will probably have changed if you've got new hardware or drivers. It looks like this - "lastdevice = ( bunch of numbers + letters here )
You will need to replace the line in your old Options file with the one from the new install options, otherwise your settings will revert to default every time you load the game.