Does booting a 2015 iMac from an external disk require "touching" the internal disk?
No, corruption like what you described here (i.e. non-hardware failure of the disk drive) does not prevent boot attempts on an external drive.

In fact you do not even need an external drive. You can just start up the iMac in Internet Recovery Mode to reformat your internal disk and reinstall macOS. You do that by holding down Command+Option+R when powering on your iMac (hold it until you see a spinning globe saying Starting Internet Recovery).