I've done it, so I know it's possible.
Some requirements:
(1) Be sure you have installed the 1.2 firmware upgrade while iMac still has Mac OS 8.6 or 9.x on it.
http://docs.info.apple.com/article.html?artnum=60384
(2) Max out RAM to 512mb. Technically 256mb is the minimum requirement, but with the slow processor, small hard drive, and low-end video hardware, you need as much RAM as possible to compensate.
(3) A FireWire external case to use with the G4 iMac.
(4) If you plan to upgrade the stock 6GB drive, understanding of the 8GB startup partition limitation for the tray-loader iMacs (and some other models). Please ask a follow-up question if you need more info about this point.
The procedure - Remove the hard drive from the tray-loader iMac. Mount it in the external FireWire case. It is already set for Master, so you should not have to change any jumper settings.
Connect the external FireWire case to the iMac G4. Start up the iMac G4 using the Tiger DVD. At the Installer's screen, you may want to go up to the menu bar to
Utilities and select to run Disk Utility. This is optional, but since the iMac's drive is old, you may want to erase it using the +Zero Out Data+ option (it's available using the
Options button on the
Erase tab). This type of erase writes zeros to all sectors, so it serves as a good +stress test+ for the drive to make sure it is working acceptably. Or you can do a normal erase.
After that completes, you have a freshly formatted drive. Quit Disk Utility to return to Installer. Select the tray-loader iMac's drive in the FireWire case as the target for the installation. Because the drive is already small, you should click on the
Customize button and deselect all component you do not need. For example, not installing languages and printer drivers you do not need can save more than a GB of disk space. Not installing apps you do not need will save even more space.
Proceed with the installation. After it completes and the iMac restarts from the external drive, you can go through the initial setup as if it was the tray-loader iMac, and make sure the installation works. You can install all the updates now or wait. It may be a good idea to wait.
Finally, remove the hard drive from the external FireWire case and mount it back into the iMac. Try to start it up. It should work. There is nothing that prevents it from working. It's only the lack of DVD drive, and (if you have the CDROM set) the Installer that checks for supported Mac model, that prevents Tiger from being installed directly on the tray-loader iMac.