mmm - theoretically it can/has been dun... but appears fraught to say the least...
Whilst generally '9x/ME like to go to the c: drive... the actual system files (the OS itself) can go elsewhere...; as long as you have corrrectly installed the boot/start-up files onto c: .
Thus if you were to boot with either a suitable '98 boot-floppy or CD to a dos (7x in this case) prompt and ensure you have usb access/support enabled (drivers installed) you may be able then to access that extrnal drive and boot to the OS thereon.
This is briefly discussed here - and does also mention that it can be a little fraught...
http://www.techspot.com/vb/topic748...
Another option requires your PC to support booting from USB...; and presuming so then one creates a bootable hd installation that is accessible at boot time via usb. Haven't gone that route (or the first approach above) so can't advise further in either regard...
Better approach? Make copy of - as in clone - your current drive (Acronis, Ghost etc...) to intended usb drive; then - if your current drive fails.. install that cloned drive in place of the failed drive?
And regardless of the above... ensure you make regular copies of all those important files etc. that you wouldn't want to lose; make them to optical media and verify they will play etc. on both the parent system and at least one other... And update those copies regularly...