Easily.
But why not just create the new folder on \\server\clients instead of creating it locally and then moving it a little later?
REM Prompt user for a folder name
SET /P NewFolder=Please Enter Folder Name:
REM Check if folder already exists - if not, create it.
IF NOT EXIST "\\server\clients\%NewFolder%" MD "\\server\clients\%NewFolder%"
REM Duplicate files in the template share in the specified folder, forcing overwrite if any already exist.
COPY "\\Server\Template\*.*" "\\server\clients\%newfolder%" /Y