I would like to upgrade my TortoiseSVN installation to version 1.7. We have a VisualSVN server running with a SVN 1.6 repository.
Do I need to upgrade the repository
Yes, it will.
You can run into problems if you use different versions of the client on the same working copy (i.e. checked out directory). Also, if you use an old client with a new server, you may not be able to use some of the new server features.
However, new SVN clients are downwards compatible with old server, with the exception of some new features. So using TortoiseSVN 1.7 with Server 1.6 should work without problems.
See the compatibility matrix on the SVN site.