Does booting a 2015 iMac from an external disk require "touching" the internal disk? The hard drive (a Fusion Drive) on my 2015 iMac has become badly corrupted, possibly getting into that state via some incompatible ram that had previous been installed in it. (The ram was removed and the computer is in its stock configuration now.) The computer won't boot past the login screen or boot into recovery mode without a kernel panic.

When I took it into have it examined by an authorized repair shop, the tech told me that because the kernel panic prevented booting into recovery mode or target disk mode, that the hard drive needed to be replaced. When I asked whether the drive could be wiped, she said no and that it was impossible without cracking open the computer.

Is this true? In a standard Windows/Linux based Intel architecture PC, any drive can simply be ignored at the bios level. Does corruption of the internal hard drive in an iMac really prevent any possible boot attempt via an external drive?
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).