Anything, anything at all, that hits a drive as intensely as something like TeskDisk does can push a failing drive to failure. Trying to defrag it could. Anything that is insanely I/O intensive could. It's not "a step" but the fact that if you have a HDD that's on the verge of physical failure, pushing it can be "the last straw." Even the cloning process could, potentially, kill it, but at least if it does you have whatever could be duplicated on to a known stable drive actually on that drive. Running something like TestDisk on a known good drive is not problematic.
So long as the disc can be read, it can be cloned.
It is possible for clones to fail, but they work somewhat differently than a straight copy, and if they fail they fail in a different way.
The reason you clone is to take the potential for actual physical drive failure of the dying drive out of the picture. You have the compromised copy (with whatever damage there was on the original) now on a stable drive. And that stable drive can be hit and hit and hit by all of the various types of recovery software of your choosing in order to get back what can be gotten back without fear of actual drive failure.
If the contents of this drive are precious I would not even do that. It would be straight off to a data recovery lab. I've seen plenty of drives that have been made unrecoverable by amateur recovery attempts that finally caused something like a head crash. You've already been hitting this drive, so the probability of total failure increases.
This situation points up, again,
Why you MUST Routinely Take Full System Image Backups of Your Computer, as a standard part of computer ownership if you value your time, sanity, and data.