Even if it is possible to recognise (1.44 MB) floppies in a USB floppy drive (when the computer is running Mac OS X 10.2.8), the problem with booting should be the same as with a USB flash drive. This would mean that you could transfer files to the internal hard disk of the original iMac G3 Bondi Blue using a USB floppy drive or a USB flash drive. You may even be able to transfer files from another appropriate Mac over a network (Ethernet, file sharing). However, according to the developer note for the original iMac, booting from USB is not supported. Booting from a drive other than the internal hard disk drive would be required in order to reformat the latter and install an operating system the normal way via an installer.
There may be some experimental ways involving system software transfers to the hard disk (especially, if access to another original iMac G3), but replacing the CD-ROM drive seems to be the only practical solution in this very case.