I tried to do this at work. The teacher purchased copies of Tiger for all her Macs, but one of them only has a CD-ROM drive while the other one has a DVD-RAM (both are Power Mac G4 systems). I used one of her G4 iBooks in Target Disk Mode (which requires a special Firewire cable) to see if I could boot up from the DVD-ROM drive in the iBook, but to no avail. It did load the hard drive and DVD once the Power Mac booted up to Panther, but I couldn't install Tiger since it needed to reboot and start from the disc.
Searching around on Google hasn't brought anything up as far as solutions. The next thing I'm going to try today is to remove the DVD-RAM from the one Power Mac G4 and install it on the one with the CD-ROM drive, that way it can boot from the DVD-RAM drive with the Tiger disc. However, since you are using a PowerBook and the DVD-ROM inside it might be hard to replace just for the quick install, I'm not sure. As you see, I couldn't get it to boot with the other computer in Target Disk Mode.
I would say try and share the optical drive from another computer on a small network, but you would still encounter the issue of having the installation begin during bootup, meaning it would have to see the network before anything and recognize the share.
Is there anyway you could actually have that PowerBook's DVD-ROM drive serviced in order to perform the upgrade?