I did experiments with root hormone last summer. I was able to get both romaine lettuce and celery to root, and for a time, actually grow. My ignorance about what makes both of those plants happy once they are growing was the major factor in their untimely deaths, I’m afraid. But I did prove rooting a store stump could be done, to my satisfaction.
I’m not sure about tarragon. All I can say, is go for it!...and report back! :-D
It will be spring when I try again—I have rooting hormone. Tarragon is good even in dry form, fortunately. Lavender, rosemary, and my deep pink crepe myrtle are all on the list of plants to try to propagate by cuttings.