can yacon grow vertically
Hello and thank you for asking about Yacón (Smallanthus sonchifolius). I am unable to find Oregon State University Extension Service information about growing this tuber in home gardens here. An educated guess is that it will not grow along the stems, as it is related to sunflowers, and the photos on the web show a clump of tubers radiating out from the crown, or base, of the plant.
However, I encourage you to do more research, perhaps finding a nursery or grower in your area with experience with this plant. Call the nurseries in your area, and also ask at farmer's markets to find experienced growers. Perhaps an internet search for your area and the plant will prove helpful, such as "Yacon Benton County Oregon", or "Yacon Corvallis".
I wish you luck with your garden, and am sorry I can't be more help to you.