Yes, it's possible.
TortoiseSVN and the svn command line client share the same settings location in your profile folder. So you may simply checkout one version using svn.exe:
$ svn co --username different_user_name file:///C:/path/to/your/repo
... and Subversion will happily replace the associated username for that repository. New commits from TortoiseSVN will then always use that username, no matter with what program you make the new checkouts.
The procedure should work with TortoiseSVN 1.5.5. If it doesn't, try emptying svn's authentication cache (%APPDATA%\Subversion\auth\svn.username
) first.