If you really want to, you can make a pipeline that unpacks the tar file on-the-fly to do the copy function:
tar -czf - /path/to/files | tee /backup/name.tar.gz | tar -C /path/to/target -xzf -
The first tar
command sends the compressed output to stdout, the tee
command makes a copy in the named file and passes the stream along to its stdout, and the final tar
command switches to the target directory and extracts the files from the stream on its stdin.