The answer to your question is No. If your Tiger system is running perfectly, just run the Leopard installer and it will overwrite Tiger and install Leopard. Then run System Update to get the latest version. However having a full backup is always a good idea.
If you aim is to obtain the latest version of iTunes you don't need Leopard (which can't run it either) but Snow Leopard, which only runs on Intel Macs.
Start by checking if you can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
OS 10.6 Snow Leopard is once again available from the Apple Store:
and in the UK:
but nobody knows for how long it will be available.