SourceTree uses folder browse dialog to select existing repository (File, Open). This prevents user from selecting network folder that is not mapped to a drive.
Choice of browse folder dialog also inhibits copy/paste of folder name.
One of solutions would be using standard dialog for folder selection on Windows Vista and above. This would be IFileDialog (http://msdn.microsoft.com/en-us/library/windows/desktop/bb775966(v=vs.85).aspx) with FOS_PICKFOLDERS flag. There is .NET example at http://www.jmedved.com/2011/12/openfolderdialog/.