No, but you could do a block copy restore of the install DVD to a small partition on either its drive, or an external HD connected to that machine.
If the 2nd machine is an Intel Mac, its drive will be partitioned using a GUID map. PPC Macs can't boot to a drive using that map - it must be APM. So, if the preceding is true, you will need an
external drive partitioned using APM (in the Disk Utility "Partition" tab, click on "Options..." to set the map type).
To make the bootable copy on your other machine's HD (or external drive), run Disk Utility and create a small (10GB should be enough) partition formatted Mac OS Extended (also making sure to set APM as the partition map type). Then, use Restore to copy the DVD to that new partition, making sure to check "erase destination" (which enables block copy).
Start up your other (2nd) Mac using FireWire Target Disk mode (hold down 'T' at startup). Now, when you startup the iMac G4, hold down the 'option', then select the partition you cloned the DVD to on your other machine. You should be able to startup on it, and during install, select the iMac's HD as the install target.
Hope that's not too confusing - I mixed "other" and "2nd" when describing your not-iMac-with-working-DVD machine. The bottom line is to access a bootable partition on that machine that you can boot off of using that machine in Target Disk Mode, connected to the iMac via FireWire.
Or, find an external FireWire DVD drive for the iMac.