Check the BIOS. If the PC can boot from USB, you should be able to add the external disk to the bootable device list (as long as it's connected and powered on). To boot from it, you'll have to install the OS, etc. You could also try to image the IDE disk, but good luck making it work.
Using an external hard disk to save important files or complete system backups makes a lot of sense, but using it as a boot disk isn't a good solution. Why not replace the IDE disk while you still can image it? You could make a complete system backup and then restore to the new IDE drive. If it works, then you know that your backup soklution works properly.