That trick you suggest, does work with a file-based repository. If your repository is stored in a database of some sorts, than all bets are off.
Verify if your setup uses a database or not, because I know from experience that SVN uses the database mode. Although Git looks like it uses file-based versioning, completely sure I am not. The same is true for Mercurial.
I personally have done this with CVS repositories. I copied the original CVS repository (all files and the .cvs folders!) from a Linux machine to a Windows machine, installed the WinNT CVS server software on the Windows PC, Then just pointed the server software to the copied repository and started the server software. That was it, all changes/comments (15 years worth!) were available.
To my understanding, you can change the mode from modern versioning software only during creation of the repository. File based repositories tend to take up more storage space than repositories that use a database. So if you have the space I would use a file based repository, for the easy backup/restore procedure.