Can bad tension damage my sewing machine?

The dial setting itself will not damage anything — you cannot turn it far enough to break a machine. What does cause damage is what happens next.

The real risk is the thread nest. A badly unbalanced stitch produces loose thread that wraps around the hook and packs into the race. Left there and sewn over, it can jam the machine mid stitch. Forcing the handwheel against that jam is one of the few things that genuinely knocks a machine out of time.

The second risk is pulling the work free. When fabric is stuck in a nest, the instinct is to pull. That bends the needle, drags the fabric against the hook, and can score the needle plate. Instead, raise the foot, cut the threads above and below, remove the needle plate, and lift the work out.

The third is a needle strike. Very tight top tension can deflect a needle enough to hit the plate or the hook. A hook with a nick in it shreds thread permanently, and replacing it is a workshop job.

What is not a risk. Sewing slowly, running the machine at a low tension setting, or leaving the dial in an unusual position. None of that stresses anything.

The habit that prevents all of it. Stop the moment the stitch looks wrong, rather than sewing on to see whether it improves. It does not improve.

Then clean the race before starting again, because the loose thread is still in there.