Time Machine Data on External Hard drive?

I am going to be doing a clean install for my friend who is currently running Leopard. He wants to keep all his music and pictures. I am bringing my external hard drive over to back up all his data.

My question involves Time Machine (which is why I was not sure if I should post here or under hardware). If I use Time Machine to back up all his data, when I do the clean install can I simply transfer all the data back on to his hard drive or will all the data be stuck on my external hard drive? I guess what I'm getting at is if it is going to require my external hard drive being plugged into his computer to access his data, I would rather just drag and drop his pics and music onto the external hard drive then just drag and drop them back after the clean install. I would prefer Time Machine just because it will keep me from having to search all over his folders trying to find all his data he wants to keep, but if it means all the data is stuck to my external hard drive, then it is of no use to me.

Any thoughts or suggestions would be appreciated. Thanks in advance.

If you do a clean install. as soon as it reboots it will ask you what you want to do next, create a user account or restore from a backup, choose restore from backup to bring back his User Account and all applications and settings onto the Macs start-up disk, just like it was before the clean install

I left out he is upgrading to Snow Leopard, then downloading Lion. But it sounds like your saying the data will be transferred back onto the Hard Drive, which is what I want to do. I know when I have done clean installs of Snow Leopard/Lion during the installation I come to a screen with four options and one is "restore from Time Machine" or something along those lines. So thanks for the quick reply