The G3 AIO and the G3 Beige have identical motherboards and ROMs, so I would lay money that disk will work fine on that machine.
The OS 9 disks should work on any machine that can run 9.0 or 9.0.4. The 8.5.1 and 8.6 disks are definitely worth trying, as, IIRC, machine locking wasn't really a thing prior to OS X. You might want to select the option to install "For any Macintosh", to make sure any necessary drivers not used on an iMac are installed.
Sidenote: 8.6 is a huge improvement in stability over 8.5.1, and should install on the same machines.
The OS 9 disks should work on any machine that can run 9.0 or 9.0.4. The 8.5.1 and 8.6 disks are definitely worth trying, as, IIRC, machine locking wasn't really a thing prior to OS X. You might want to select the option to install "For any Macintosh", to make sure any necessary drivers not used on an iMac are installed.
Sidenote: 8.6 is a huge improvement in stability over 8.5.1, and should install on the same machines.